Question

Thực hiện các phép tính sau

(2x³-21x²+67x-60):(x-5)

(x⁴+2x³+x-25):(x²+5)

(27x³-8):(6x+9x²+4)

Answer 1

1.

$2x^3-21x^2+67x-60=2x^2(x-5)-11x(x-5)+12(x-5)$

$=(x-5)(2x^2-11x+12)$

$\Rightarrow (2x^3-21x^2+67x-60):(x-5)=2x^2-11x+12$

Answer 2

2.

$x^4+2x^3+x-25=x^2(x^2+5)+2x(x^2+5)-5x^2-9x-25$

$=x^2(x^2+5)+2x(x^2+5)-5(x^2+5)-9x=(x^2+5)(x^2+2x-5)-9x$

$\Rightarrow (x^4+2x^3+x-25):(x^2+5)=x^2+2x-5$ và dư $-9x$

Answer 3

3.

$27x^3-8=(3x)^3-2^3=(3x-2)(9x^2+6x+4)$

$\Rightarrow (27x^3-8):(9x^2+6x+4)=3x-2$