与えられた8つの二次式を因数分解する問題です。 (1) $2x^2 - 7x + 3$ (2) $2x^2 + 13x + 6$ (3) $9x^2 - 3x - 2$ (4) $6x^2 - 5x - 6$ (5) $6x^2 + 7xy + y^2$ (6) $3x^2 - 5xy - 2y^2$ (7) $6x^2 + xy - 2y^2$ (8) $9x^2 + xy - 10y^2$

1. 問題の内容

与えられた8つの二次式を因数分解する問題です。

(1) $2x^2 - 7x + 3$

(2) $2x^2 + 13x + 6$

(3) $9x^2 - 3x - 2$

(4) $6x^2 - 5x - 6$

(5) $6x^2 + 7xy + y^2$

(6) $3x^2 - 5xy - 2y^2$

(7) $6x^2 + xy - 2y^2$

(8) $9x^2 + xy - 10y^2$

2. 解き方の手順

各二次式を因数分解します。

(1) $2x^2 - 7x + 3$

$2x^2 - 6x - x + 3 = 2x(x - 3) - 1(x - 3) = (2x - 1)(x - 3)$

(2) $2x^2 + 13x + 6$

$2x^2 + 12x + x + 6 = 2x(x + 6) + 1(x + 6) = (2x + 1)(x + 6)$

(3) $9x^2 - 3x - 2$

$9x^2 - 6x + 3x - 2 = 3x(3x - 2) + 1(3x - 2) = (3x + 1)(3x - 2)$

(4) $6x^2 - 5x - 6$

$6x^2 - 9x + 4x - 6 = 3x(2x - 3) + 2(2x - 3) = (3x + 2)(2x - 3)$

(5) $6x^2 + 7xy + y^2$

$6x^2 + 6xy + xy + y^2 = 6x(x + y) + y(x + y) = (6x + y)(x + y)$

(6) $3x^2 - 5xy - 2y^2$

$3x^2 - 6xy + xy - 2y^2 = 3x(x - 2y) + y(x - 2y) = (3x + y)(x - 2y)$

(7) $6x^2 + xy - 2y^2$

$6x^2 + 4xy - 3xy - 2y^2 = 2x(3x + 2y) - y(3x + 2y) = (2x - y)(3x + 2y)$

(8) $9x^2 + xy - 10y^2$

$9x^2 + 10xy - 9xy - 10y^2 = x(9x + 10y) - y(9x + 10y) = (x-y)(9x+10y)$

$9x^2 + 10xy - 9xy - 10y^2 = 9x(x-y) + 10y(x-y) = (9x + 10y)(x-y)$

3. 最終的な答え

(1) $(2x - 1)(x - 3)$

(2) $(2x + 1)(x + 6)$

(3) $(3x + 1)(3x - 2)$

(4) $(3x + 2)(2x - 3)$

(5) $(6x + y)(x + y)$

(6) $(3x + y)(x - 2y)$

(7) $(2x - y)(3x + 2y)$

(8) $(9x + 10y)(x - y)$