第1章前提知識Prerequisites

Answer Key解答

Solution 1解答 1

ⓐ $\frac{11}{1}$ ⓑ $\frac{3}{1}$ ⓒ $- \frac{4}{1}$

Solution 2解答 2

ⓐ4 (or 4.0), terminating;ⓑ $0. \bar{615384},$ repeating;ⓒ–0.85, terminating

ⓐ4(または4.0)、有限小数ⓑ $0. \bar{615384}$ 循環小数ⓒ–0.85、有限小数

Solution 3解答 3

ⓐrational and repeating;ⓑrational and terminating;ⓒirrational;ⓓrational and terminating;ⓔirrational

ⓐ有理数で循環小数ⓑ有理数で有限小数ⓒ無理数ⓓ有理数で有限小数ⓔ無理数

Solution 4解答 4

ⓐpositive, irrational; rightⓑnegative, rational; leftⓒpositive, rational; rightⓓnegative, irrational; leftⓔpositive, rational; right

ⓐ正で無理数。右ⓑ負で有理数。左ⓒ正で有理数。右ⓓ負で無理数。左ⓔ正で有理数。右

Solution 5解答 5

	N	W	I	Q	Q'
a. $- \frac{35}{7}$			X	X
b. 0		X	X	X
c. $\sqrt{169}$	X	X	X	X
d. $\sqrt{24}$					X
e. 4.763763763...				X

Solution 6解答 6

ⓐ10ⓑ2ⓒ4.5ⓓ25ⓔ26

Solution 7解答 7

ⓐ11, commutative property of multiplication, associative property of multiplication, inverse property of multiplication, identity property of multiplication;ⓑ33, distributive property;ⓒ26, distributive property;ⓓ $\frac{4}{9},$ commutative property of addition, associative property of addition, inverse property of addition, identity property of addition;ⓔ0, distributive property, inverse property of addition

ⓐ11。乗法の交換法則、乗法の結合法則、乗法の逆元の法則、乗法の単位元の法則ⓑ33。分配法則ⓒ26。分配法則ⓓ $\frac{4}{9}$ 加法の交換法則、加法の結合法則、加法の逆元の法則、加法の単位元の法則ⓔ0。分配法則、加法の逆元の法則

Solution 8解答 8

	Constants定数	Variables変数
a. $2 π r (r + h)$	$2, π$	$r, h$
b. 2(L + W)	2	L, W
c. $4 y^{3} + y$	4	$y$

Solution 9解答 9

ⓐ5;ⓑ11;ⓒ9;ⓓ26

Solution 10解答 10

ⓐ4;ⓑ11;ⓒ $\frac{121}{3} π$ ;ⓓ1728;ⓔ3

Solution 11解答 11

1,152 cm²

Solution 12解答 12

ⓐ $−2 y −2 z or −2 (y + z);$ ⓑ $\frac{2}{t} −1;$ ⓒ $3 p q −4 p + q;$ ⓓ $7 r −2 s + 6$

式中の英語：or：または

Solution 13解答 13

$A = P (1 + r t)$

Solution 1解答 1

ⓐ $k^{15}$ ⓑ ${(\frac{2}{y})}^{5}$ ⓒ $t^{14}$

Solution 2解答 2

ⓐ $s^{7}$ ⓑ ${(−3)}^{5}$ ⓒ ${(e f^{2})}^{2}$

Solution 3解答 3

ⓐ ${(3 y)}^{24}$ ⓑ $t^{35}$ ⓒ ${(- g)}^{16}$

Solution 4解答 4

ⓐ $1$ ⓑ $\frac{1}{2}$ ⓒ $1$ ⓓ $1$

Solution 5解答 5

ⓐ $\frac{1}{{(−3 t)}^{6}}$ ⓑ $\frac{1}{f^{3}}$ ⓒ $\frac{2}{5 k^{3}}$

Solution 6解答 6

ⓐ $t^{−5} = \frac{1}{t^{5}}$ ⓑ $\frac{1}{25}$

Solution 7解答 7

ⓐ $g^{10} h^{15}$ ⓑ $125 t^{3}$ ⓒ $−27 y^{15}$ ⓓ $\frac{1}{a^{18} b^{21}}$ ⓔ $\frac{r^{12}}{s^{8}}$

Solution 8解答 8

ⓐ $\frac{b^{15}}{c^{3}}$ ⓑ $\frac{625}{u^{32}}$ ⓒ $\frac{−1}{w^{105}}$ ⓓ $\frac{q^{24}}{p^{32}}$ ⓔ $\frac{1}{c^{20} d^{12}}$

Solution 9解答 9

ⓐ $\frac{v^{6}}{8 u^{3}}$ ⓑ $\frac{1}{x^{3}}$ ⓒ $\frac{e^{4}}{f^{4}}$ ⓓ $\frac{27 r}{s}$ ⓔ $1$ ⓕ $\frac{16 h^{10}}{49}$

Solution 10解答 10

ⓐ $$ 1.52 \times 10^{5}$ ⓑ $7.158 \times 10^{9}$ ⓒ $$ 8.55 \times 10^{13}$ ⓓ $3.34 \times 10^{−9}$ ⓔ $7.15 \times 10^{−8}$

Solution 11解答 11

ⓐ $703, 000$ ⓑ $−816, 000, 000, 000$ ⓒ $−0.000 000 000 000 39$ ⓓ $0.000008$

Solution 12解答 12

ⓐ $- 8.475 \times 10^{6}$ ⓑ $8 \times 10^{- 8}$ ⓒ $2.976 \times 10^{13}$ ⓓ $- 4.3 \times 10^{6}$ ⓔ $\approx 1.24 \times 10^{15}$

Solution 13解答 13

Number of cells: $3 \times 10^{13};$ length of a cell: $8 \times 10^{−6}$ m; total length: $2.4 \times 10^{8}$ m or $240, 000, 000$ m.

細胞の数 $3 \times 10^{13};$ 、細胞1個の長さ $8 \times 10^{−6}$ m、全長 $2.4 \times 10^{8}$ m すなわち $240, 000, 000$ m。

Solution 1解答 1

ⓐ $15$ ⓑ $3$ ⓒ $4$ ⓓ $17$

Solution 2解答 2

$5 | x | | y | \sqrt{2 y z} .$ Notice the absolute value signs around x and y? That’s because their value must be positive!

$5 | x | | y | \sqrt{2 y z}$ x と y に絶対値の記号が付いていることに気づいたか。値が正でなければならないからである。

Solution 3解答 3

$10 | x |$

Solution 4解答 4

$\frac{x \sqrt{2}}{3 y^{2}} .$ We do not need the absolute value signs for $y^{2}$ because that term will always be nonnegative.

$\frac{x \sqrt{2}}{3 y^{2}}$ $y^{2}$ には絶対値の記号は要らない。その項はつねに非負だからである。

Solution 5解答 5

$b^{4} \sqrt{3 a b}$

Solution 6解答 6

$13 \sqrt{5}$

Solution 7解答 7

$0$

Solution 8解答 8

$6 \sqrt{6}$

Solution 9解答 9

$14 −7 \sqrt{3}$

Solution 10解答 10

ⓐ $−6$ ⓑ $6$ ⓒ $88 \sqrt[3]{9}$

Solution 11解答 11

${(\sqrt{9})}^{5} = 3^{5} = 243$

Solution 12解答 12

$x {(5 y)}^{\frac{9}{2}}$

Solution 13解答 13

$28 x^{\frac{23}{15}}$

Solution 1解答 1

The degree is 6, the leading term is $- x^{6},$ and the leading coefficient is $−1.$

次数は6、最高次の項は $- x^{6}$ 、最高次係数は $−1.$

Solution 2解答 2

$2 x^{3} + 7 x^{2} −4 x −3$

Solution 3解答 3

$−11 x^{3} - x^{2} + 7 x −9$

Solution 4解答 4

$3 x^{4} −10 x^{3} −8 x^{2} + 21 x + 14$

Solution 5解答 5

$3 x^{2} + 16 x −35$

Solution 6解答 6

$16 x^{2} −8 x + 1$

Solution 7解答 7

$4 x^{2} −49$

Solution 8解答 8

$6 x^{2} + 21 x y −29 x −7 y + 9$

Solution 1解答 1

$(b^{2} - a) (x + 6)$

Solution 2解答 2

$(x −6) (x −1)$

Solution 3解答 3

ⓐ $(2 x + 3) (x + 3)$ ⓑ $(3 x −1) (2 x + 1)$

Solution 4解答 4

${(7 x −1)}^{2}$

Solution 5解答 5

$(9 y + 10) (9 y - 10)$

Solution 6解答 6

$(6 a + b) (36 a^{2} −6 a b + b^{2})$

Solution 7解答 7

$(10 x - 1) (100 x^{2} + 10 x + 1)$

Solution 8解答 8

${(5 a −1)}^{- \frac{1}{4}} (17 a −2)$

Solution 1解答 1

$\frac{1}{x + 6}$

Solution 2解答 2

$\frac{(x + 5) (x + 6)}{(x + 2) (x + 4)}$

Solution 3解答 3

$1$

Solution 4解答 4

$\frac{2 (x −7)}{(x + 5) (x −3)}$

Solution 5解答 5

$\frac{x^{2} - y^{2}}{x y^{2}}$

1.1 Section Exercises1.1 節末問題

Solution 1解答 1

irrational number. The square root of two does not terminate, and it does not repeat a pattern. It cannot be written as a quotient of two integers, so it is irrational.

無理数。2の平方根は有限小数にならず、決まった並びの繰り返しにもならない。二つの整数の商としては書けないので、無理数である。

Solution 3解答 3

The Associative Properties state that the sum or product of multiple numbers can be grouped differently without affecting the result. This is because the same operation is performed (either addition or subtraction), so the terms can be re-ordered.

結合法則は、複数の数の和や積は、まとめ方を変えても結果が変わらないと述べる。行う演算が同じ(加法どうし、あるいは減法どうし)なので、項の順序を入れ替えられるからである。

Solution 5解答 5

$−6$

Solution 7解答 7

$−2$

Solution 9解答 9

$−9$

Solution 11解答 11

Solution 13解答 13

-2

Solution 15解答 15

Solution 17解答 17

Solution 19解答 19

Solution 21解答 21

Solution 23解答 23

$−6$

Solution 25解答 25

Solution 27解答 27

Solution 29解答 29

$14$

Solution 31解答 31

$−66$

Solution 33解答 33

$–12$

Solution 35解答 35

$–44$

Solution 37解答 37

$–2$

Solution 39解答 39

$−14 y - 11$

Solution 41解答 41

$−4 b + 1$

Solution 43解答 43

$43 z - 3$

Solution 45解答 45

$9 y + 45$

Solution 47解答 47

$−6 b + 6$

Solution 49解答 49

$\frac{16 x}{3}$

Solution 51解答 51

$9 x$

Solution 53解答 53

$\frac{1}{2} (40 - 10) + 5$

Solution 55解答 55

irrational number

無理数

Solution 57解答 57

$g + 400 - 2 (600) = 1200$

Solution 59解答 59

inverse property of addition

加法の逆元の法則

Solution 61解答 61

68.4

Solution 63解答 63

true

正しい

Solution 65解答 65

irrational

無理数

Solution 67解答 67

rational

有理数

1.2 Section Exercises1.2 節末問題

Solution 1解答 1

No, the two expressions are not the same. An exponent tells how many times you multiply the base. So $2^{3}$ is the same as $2 \times 2 \times 2,$ which is 8. $3^{2}$ is the same as $3 \times 3,$ which is 9.

いいえ。二つの式は同じではない。指数は底を何回掛けるかを示す。だから $2^{3}$ は $2 \times 2 \times 2$ と同じで8になる。 $3^{2}$ は $3 \times 3$ と同じで9になる。

Solution 3解答 3

It is a method of writing very small and very large numbers.

とても小さい数やとても大きい数を書く方法である。

Solution 5解答 5

Solution 7解答 7

243

Solution 9解答 9

$\frac{1}{16}$

Solution 11解答 11

$\frac{1}{11}$

Solution 13解答 13

Solution 15解答 15

$4^{9}$

Solution 17解答 17

$12^{40}$

Solution 19解答 19

$\frac{1}{7^{9}}$

Solution 21解答 21

$3.14 \times 10^{- 5}$

Solution 23解答 23

16,000,000,000

Solution 25解答 25

$a^{4}$

Solution 27解答 27

$b^{6} c^{8}$

Solution 29解答 29

$a b^{2} d^{3}$

Solution 31解答 31

$m^{4}$

Solution 33解答 33

$\frac{q^{5}}{p^{6}}$

Solution 35解答 35

$\frac{y^{21}}{x^{14}}$

Solution 37解答 37

$25$

Solution 39解答 39

$72 a^{2}$

Solution 41解答 41

$\frac{c^{3}}{b^{9}}$

Solution 43解答 43

$\frac{y}{81 z^{6}}$

Solution 45解答 45

0.00135 m

Solution 47解答 47

$1.0995 \times 10^{12}$

Solution 49解答 49

0.00000000003397 in.

0.00000000003397 インチ

Solution 51解答 51

12,230,590,464 $m^{66}$

Solution 53解答 53

$\frac{a^{14}}{1296}$

Solution 55解答 55

$\frac{n}{a^{9} c}$

Solution 57解答 57

$\frac{1}{a^{6} b^{6} c^{6}}$

Solution 59解答 59

0.000000000000000000000000000000000662606957

1.3 Section Exercises1.3 節末問題

Solution 1解答 1

When there is no index, it is assumed to be 2 or the square root. The expression would only be equal to the radicand if the index were 1.

根号の指数が書かれていないときは、2すなわち平方根とみなす。この式が根号の中身に等しくなるのは、指数が1のときだけである。

Solution 3解答 3

The principal square root is the nonnegative root of the number.

正の平方根とは、その数の根のうち非負のものである。

Solution 5解答 5

Solution 7解答 7

Solution 9解答 9

Solution 11解答 11

$7 \sqrt{2}$

Solution 13解答 13

$\frac{9 \sqrt{5}}{5}$

Solution 15解答 15

Solution 17解答 17

$\sqrt{2}$

Solution 19解答 19

$2 \sqrt{6}$

Solution 21解答 21

$5 \sqrt{6}$

Solution 23解答 23

$6 \sqrt{35}$

Solution 25解答 25

$\frac{2}{15}$

Solution 27解答 27

$\frac{6 \sqrt{10}}{19}$

Solution 29解答 29

$- \frac{1 + \sqrt{17}}{2}$

Solution 31解答 31

$7 \sqrt[3]{2}$

Solution 33解答 33

$15 \sqrt{5}$

Solution 35解答 35

$20 x^{2}$

Solution 37解答 37

$7 \sqrt{p}$

Solution 39解答 39

$17 m^{2} \sqrt{m}$

Solution 41解答 41

$2 b \sqrt{a}$

Solution 43解答 43

$\frac{15 x}{7}$

Solution 45解答 45

$5 y^{4} \sqrt{2}$

Solution 47解答 47

$\frac{4 \sqrt{7 d}}{7 d}$

Solution 49解答 49

$\frac{2 \sqrt{2} + 2 \sqrt{6 x}}{1 −3 x}$

Solution 51解答 51

$- w \sqrt{2 w}$

Solution 53解答 53

$\frac{3 \sqrt{x} - \sqrt{3 x}}{2}$

Solution 55解答 55

$5 n^{5} \sqrt{5}$

Solution 57解答 57

$\frac{9 \sqrt{m}}{19 m}$

Solution 59解答 59

$\frac{2}{3 d}$

Solution 61解答 61

$\frac{3 \sqrt[4]{2 x^{2}}}{2}$

Solution 63解答 63

$6 z \sqrt[3]{2}$

Solution 65解答 65

500 feet

500フィート

Solution 67解答 67

$\frac{−5 \sqrt{2} −6}{7}$

Solution 69解答 69

$\frac{\sqrt{m n c}}{a^{9} c m n}$

Solution 71解答 71

$\frac{2 x + 1}{2 \sqrt{2}}$

Solution 73解答 73

$\frac{\sqrt{3}}{3}$

1.4 Section Exercises1.4 節末問題

Solution 1解答 1

The statement is true. In standard form, the polynomial with the highest value exponent is placed first and is the leading term. The degree of a polynomial is the value of the highest exponent, which in standard form is also the exponent of the leading term.

この文は正しい。標準形では、指数の値がいちばん大きい項が先頭に置かれ、それが最高次の項になる。多項式の次数はいちばん大きい指数の値であり、標準形ではそれが最高次の項の指数でもある。

Solution 3解答 3

Use the distributive property, multiply, combine like terms, and simplify.

分配法則を使い、掛け、同類項をまとめ、簡単にする。

Solution 5解答 5

Solution 7解答 7

Solution 9解答 9

Solution 11解答 11

$4 x^{2} + 3 x + 19$

Solution 13解答 13

$3 w^{2} + 30 w + 21$

Solution 15解答 15

$11 b^{4} −9 b^{3} + 12 b^{2} −7 b + 8$

Solution 17解答 17

$24 x^{2} −4 x −8$

Solution 19解答 19

$24 b^{4} −48 b^{2} + 24$

Solution 21解答 21

$99 v^{2} −202 v + 99$

Solution 23解答 23

$8 n^{3} −4 n^{2} + 72 n −36$

Solution 25解答 25

$9 y^{2} −42 y + 49$

Solution 27解答 27

$16 p^{2} + 72 p + 81$

Solution 29解答 29

$9 y^{2} −36 y + 36$

Solution 31解答 31

$16 c^{2} −1$

Solution 33解答 33

$225 n^{2} −36$

Solution 35解答 35

$−16 m^{2} + 16$

Solution 37解答 37

$121 q^{2} −100$

Solution 39解答 39

$16 t^{4} + 4 t^{3} −32 t^{2} - t + 7$

Solution 41解答 41

$y^{3} −6 y^{2} - y + 18$

Solution 43解答 43

$3 p^{3} - p^{2} −12 p + 10$

Solution 45解答 45

$a^{2} - b^{2}$

Solution 47解答 47

$16 t^{2} −40 t u + 25 u^{2}$

Solution 49解答 49

$4 t^{2} + x^{2} + 4 t −5 t x - x$

Solution 51解答 51

$24 r^{2} + 22 r d −7 d^{2}$

Solution 53解答 53

$32 x^{2} −4 x −3$ m²

Solution 55解答 55

$32 t^{3} - 100 t^{2} + 40 t + 38$

Solution 57解答 57

$a^{4} + 4 a^{3} c −16 a c^{3} −16 c^{4}$

1.5 Section Exercises1.5 節末問題

Solution 1解答 1

The terms of a polynomial do not have to have a common factor for the entire polynomial to be factorable. For example, $4 x^{2}$ and $−9 y^{2}$ don’t have a common factor, but the whole polynomial is still factorable: $4 x^{2} −9 y^{2} = (2 x + 3 y) (2 x −3 y) .$

多項式全体が因数分解できるために、項に共通の因数がある必要はない。たとえば $4 x^{2}$ と $−9 y^{2}$ には共通の因数が無いが、多項式全体は因数分解できる。 $4 x^{2} −9 y^{2} = (2 x + 3 y) (2 x −3 y)$

Solution 3解答 3

Divide the $x$ term into the sum of two terms, factor each portion of the expression separately, and then factor out the GCF of the entire expression.

$x$ の項を二つの項の和に分け、式のそれぞれの部分を別々に因数分解し、最後に式全体の GCF をくくり出す。

Solution 5解答 5

$7 m$

Solution 7解答 7

$10 m^{3}$

Solution 9解答 9

$y$

Solution 11解答 11

$(2 a −3) (a + 6)$

Solution 13解答 13

$(3 n −11) (2 n + 1)$

Solution 15解答 15

$(p + 1) (2 p −7)$

Solution 17解答 17

$(5 h + 3) (2 h −3)$

Solution 19解答 19

$(9 d −1) (d −8)$

Solution 21解答 21

$(12 t + 13) (t −1)$

Solution 23解答 23

$(4 x + 10) (4 x - 10)$

Solution 25解答 25

$(11 p + 13) (11 p - 13)$

Solution 27解答 27

$(19 d + 9) (19 d - 9)$

Solution 29解答 29

$(12 b + 5 c) (12 b - 5 c)$

Solution 31解答 31

${(7 n + 12)}^{2}$

Solution 33解答 33

${(15 y + 4)}^{2}$

Solution 35解答 35

${(5 p - 12)}^{2}$

Solution 37解答 37

$(x + 6) (x^{2} - 6 x + 36)$

Solution 39解答 39

$(5 a + 7) (25 a^{2} - 35 a + 49)$

Solution 41解答 41

$(4 x - 5) (16 x^{2} + 20 x + 25)$

Solution 43解答 43

$(5 r + 12 s) (25 r^{2} - 60 r s + 144 s^{2})$

Solution 45解答 45

${(2 c + 3)}^{- \frac{1}{4}} (−7 c - 15)$

Solution 47解答 47

${(x + 2)}^{- \frac{2}{5}} (19 x + 10)$

Solution 49解答 49

${(2 z - 9)}^{- \frac{3}{2}} (27 z - 99)$

Solution 51解答 51

$(14 x −3) (7 x + 9)$

Solution 53解答 53

$(3 x + 5) (3 x −5)$

Solution 55解答 55

${(2 x + 5)}^{2} {(2 x - 5)}^{2}$

Solution 57解答 57

$(4 z^{2} + 49 a^{2}) (2 z + 7 a) (2 z - 7 a)$

Solution 59解答 59

$\frac{1}{(4 x + 9) (4 x −9) (2 x + 3)}$

1.6 Section Exercises1.6 節末問題

Solution 1解答 1

You can factor the numerator and denominator to see if any of the terms can cancel one another out.

分子と分母を因数分解して、打ち消し合う項がないかを見ればよい。

Solution 3解答 3

True. Multiplication and division do not require finding the LCD because the denominators can be combined through those operations, whereas addition and subtraction require like terms.

正しい。乗法と除法では、その演算によって分母どうしをまとめられるので LCD を求める必要がない。一方、加法と減法には同類項が要る。

Solution 5解答 5

$\frac{y + 5}{y + 6}$

Solution 7解答 7

$3 b + 3$

Solution 9解答 9

$\frac{x + 4}{2 x + 2}$

Solution 11解答 11

$\frac{a + 3}{a - 3}$

Solution 13解答 13

$\frac{3 n - 8}{7 n - 3}$

Solution 15解答 15

$\frac{c - 6}{c + 6}$

Solution 17解答 17

$1$

Solution 19解答 19

$\frac{d^{2} - 25}{25 d^{2} - 1}$

Solution 21解答 21

$\frac{t + 5}{t + 3}$

Solution 23解答 23

$\frac{6 x - 5}{6 x + 5}$

Solution 25解答 25

$\frac{p + 6}{4 p + 3}$

Solution 27解答 27

$\frac{2 d + 9}{d + 11}$

Solution 29解答 29

$\frac{12 b + 5}{3 b −1}$

Solution 31解答 31

$\frac{4 y −1}{y + 4}$

Solution 33解答 33

$\frac{10 x + 4 y}{x y}$

Solution 35解答 35

$\frac{9 a - 7}{a^{2} - 2 a - 3}$

Solution 37解答 37

$\frac{2 y^{2} - y + 9}{y^{2} - y - 2}$

Solution 39解答 39

$\frac{5 z^{2} + z + 5}{z^{2} - z - 2}$

Solution 41解答 41

$\frac{x + 2 x y + y}{x + x y + y + 1}$

Solution 43解答 43

$\frac{2 b + 7 a}{a b^{2}}$

Solution 45解答 45

$\frac{18 + a b}{4 b}$

Solution 47解答 47

$a - b$

Solution 49解答 49

$\frac{3 c^{2} + 3 c - 2}{2 c^{2} + 5 c + 2}$

Solution 51解答 51

$\frac{15 x + 7}{x −1}$

Solution 53解答 53

$\frac{x + 9}{x −9}$

Solution 55解答 55

$\frac{1}{y + 2}$

Solution 57解答 57

$4$

Review Exercises復習問題

Solution 1解答 1

$−5$

Solution 3解答 3

Solution 5解答 5

$y = 24$

Solution 7解答 7

$32 m$

Solution 9解答 9

whole

非負整数

Solution 11解答 11

irrational

無理数

Solution 13解答 13

$16$

Solution 15解答 15

$3 a^{6}$

Solution 17解答 17

$\frac{x^{3}}{32 y^{3}}$

Solution 19解答 19

$a$

Solution 21解答 21

$1.634 \times 10^{7}$

Solution 23解答 23

Solution 25解答 25

$5 \sqrt{3}$

Solution 27解答 27

$\frac{4 \sqrt{2}}{5}$

Solution 29解答 29

$\frac{7 \sqrt{2}}{50}$

Solution 31解答 31

$10 \sqrt{3}$

Solution 33解答 33

$−3$

Solution 35解答 35

$3 x^{3} + 4 x^{2} + 6$

Solution 37解答 37

$5 x^{2} - x + 3$

Solution 39解答 39

$k^{2} - 3 k - 18$

Solution 41解答 41

$x^{3} + x^{2} + x + 1$

Solution 43解答 43

$3 a^{2} + 5 a b - 2 b^{2}$

Solution 45解答 45

$9 p$

Solution 47解答 47

$4 a^{2}$

Solution 49解答 49

$(4 a - 3) (2 a + 9)$

Solution 51解答 51

${(x + 5)}^{2}$

Solution 53解答 53

${(2 h - 3 k)}^{2}$

Solution 55解答 55

$(p + 6) (p^{2} - 6 p + 36)$

Solution 57解答 57

$(4 q - 3 p) (16 q^{2} + 12 p q + 9 p^{2})$

Solution 59解答 59

${(p + 3)}^{\frac{1}{3}} (−5 p - 24)$

Solution 61解答 61

$\frac{x + 3}{x - 4}$

Solution 63解答 63

$\frac{1}{2}$

Solution 65解答 65

$\frac{m + 2}{m - 3}$

Solution 67解答 67

$\frac{6 x + 10 y}{x y}$

Solution 69解答 69

$\frac{1}{6}$

Practice Test実力テスト

Solution 1解答 1

rational

有理数

Solution 3解答 3

$x = –2$

Solution 5解答 5

3,141,500

Solution 7解答 7

$16$

Solution 9解答 9

Solution 11解答 11

$2 x$

Solution 13解答 13

Solution 15解答 15

$\frac{3 \sqrt{x}}{4}$

Solution 17解答 17

$21 \sqrt{6}$

Solution 19解答 19

$13 q^{3} - 4 q^{2} - 5 q$

Solution 21解答 21

$n^{3} - 6 n^{2} + 12 n - 8$

Solution 23解答 23

$(4 x + 9) (4 x - 9)$

Solution 25解答 25

$(3 c - 11) (9 c^{2} + 33 c + 121)$

Solution 27解答 27

$\frac{4 z - 3}{2 z - 1}$

Solution 29解答 29

$\frac{3 a + 2 b}{3 b}$