1079 Вправа 1079Алгебра 8 клас Бевз 2025 · § 21 · стор. 204

1079. Factoring the quadratic trinomial. a) x² − 3x + 2; b) x² − 2x − 35; c) −x² + 5x − 6; d) x² − 7x + 6; e) 9x² − 12x + 4; f) y² + 2y − 8.

a) ${\displaystyle x^2-3x+2}$: ${\displaystyle x_1+x_2=}$${\displaystyle 3}$;

${\displaystyle x_1{x}_2=}$${\displaystyle 2}$ → ${\displaystyle x_1=}$${\displaystyle 2,x_2=}$${\displaystyle 1}$;

${\displaystyle x^2-3x+2=}$${\displaystyle \left(x-2\right)\left(x-1\right)}$;

b) ${\displaystyle x^2-2x-35}$: ${\displaystyle x_1+x_2=}$${\displaystyle 2}$;

${\displaystyle x_1{x}_2=}$${\displaystyle -35}$ → ${\displaystyle x_1=}$${\displaystyle 7,x_2=}$${\displaystyle -5}$;

${\displaystyle x^2-2x-35=}$${\displaystyle \left(x-7\right)\left(x+5\right)}$;

c) ${\displaystyle -x^2+5x-6}$: ${\displaystyle D=}$${\displaystyle 5^2-4\cdot (-1)\cdot (-6)=}$${\displaystyle 1}$;

${\displaystyle x_{1,2}=}$${\displaystyle \frac{-5\pm 1}{-2}}$;

${\displaystyle x_1=}$${\displaystyle 3}$;

${\displaystyle x_2=}$${\displaystyle 2}$;

${\displaystyle -x^2+5x-6=}$${\displaystyle -\left(x-3\right)\left(x-2\right)}$;

d) ${\displaystyle x^2-7x+6}$: ${\displaystyle x_1+x_2=}$${\displaystyle 7}$;

${\displaystyle x_1{x}_2=}$${\displaystyle 6}$ → ${\displaystyle x_1=}$${\displaystyle 6,x_2=}$${\displaystyle 1}$;

${\displaystyle x^2-7x+6=}$${\displaystyle \left(x-6\right)\left(x-1\right)}$;

e) ${\displaystyle 9x^2-12x+4}$: ${\displaystyle D=}$${\displaystyle {(-12)}^2-4\cdot 9\cdot 4=}$${\displaystyle 0}$;

${\displaystyle x_0=}$${\displaystyle \frac{12}{18}=}$${\displaystyle \frac{2}{3}}$;

${\displaystyle 9x^2-12x+4=}$${\displaystyle 9{(x-\frac{2}{3})}^2=}$${\displaystyle {\left(3x-2\right)}^2}$;

f) ${\displaystyle y^2+2y-8}$: ${\displaystyle y_1+y_2=}$${\displaystyle -2}$;

${\displaystyle y_1{y}_2=}$${\displaystyle -8}$ → ${\displaystyle y_1=}$${\displaystyle 2,y_2=}$${\displaystyle -4}$;

${\displaystyle y^2+2y-8=}$${\displaystyle \left(y-2\right)\left(y+4\right)}$.