810° Вправа 810Алгебра 8 клас Тарасенкова 2025 · § 20 · стор. 242

810. Запишіть розклад деякого квадратного тричлена на лінійні множники, якщо:

1) ${\displaystyle a=}$${\displaystyle 1}$, ${\displaystyle x_1=}$${\displaystyle 3}$, ${\displaystyle x_2=}$${\displaystyle 5}$;

${\displaystyle a(x-x_1)(x-x_2)=}$${\displaystyle \left(x-3\right)\left(x-5\right)}$;

2) ${\displaystyle a=}$${\displaystyle 1}$, ${\displaystyle x_1=}$${\displaystyle -2}$, ${\displaystyle x_2=}$${\displaystyle 4}$;

${\displaystyle a(x-x_1)(x-x_2)=}$${\displaystyle \left(x+2\right)\left(x-4\right)}$;

3) ${\displaystyle a=}$${\displaystyle 2}$, ${\displaystyle x_1=}$${\displaystyle 3}$, ${\displaystyle x_2=}$${\displaystyle -3}$;

${\displaystyle a(x-x_1)(x-x_2)=}$${\displaystyle 2\left(x-3\right)\left(x+3\right)}$;

4) ${\displaystyle a=}$${\displaystyle -3}$, ${\displaystyle x_1=}$${\displaystyle 1}$, ${\displaystyle x_2=}$${\displaystyle \frac{1}{3}}$;

${\displaystyle a(x-x_1)(x-x_2)=}$${\displaystyle -3\left(x-1\right)\left(x-\frac{1}{3}\right)}$.