Câu hỏi của Aiko Akira Akina

Question

Phân tích đa thức thành nhiều hạng tử:

a)x4+x3+x+1

b)x4-x3-x2+1

c) (2x+1)2-(x-1)2

d) x4+4x2-5

Dung Nguyễn Thị Xuân · Accepted Answer

a) $x^4+x^3+x+1$

$=x^3\left(x+1\right)+\left(x+1\right)$

$=\left(x+1\right)\left(x^3+1\right)$

$=\left(x+1\right)^2\left(x^2-x+1\right)$

b) $x^4-x^3-x^2+1$

$=x^3\left(x-1\right)-\left(x^2-1\right)$

$=x^3\left(x-1\right)-\left(x+1\right)\left(x-1\right)$

$=\left(x-1\right)\left(x^3-x-1\right)$

c) $\left(2x+1\right)^2-\left(x-1\right)^2$

$=\left(2x+1+x-1\right)\left(2x+1-x+1\right)$

$=3x\left(x+2\right)$

d) $x^4+4x^2-5$

$=\left(x^4+4x^2+4\right)-9$

$=\left(x^2+2\right)^2-9$

$=\left(x^2+5\right)\left(x^2-1\right)$

$=\left(x^2+5\right)\left(x+1\right)\left(x-1\right)$Câu trả lời: a) $x^4+x^3+x+1$