Câu hỏi của Khánh Vân

Question

phân tích đa thức thành nhân tử
a, a4 - 4a3 + 8a2 - 16a + 16
b, x3 - 3x2 - 7x - 15
c, x5 - x4 - 10x3 - 38x2 - 51x - 45

Nguyễn Nam · Accepted Answer

a) $a^4-4a^3+8a^2-16a+16$

$=a^4-4a^3+4a^2+4a^2-16a+16$

$=\left(a^4-4a^3+4a^2\right)+\left(4a^2-16a+16\right)$

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

$=a^2\left(a^2-2.a.2+2^2\right)+4\left(a^2-2.a.2+2^2\right)$

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

$=\left(a-2\right)^2\left(a^2+4\right)$Câu trả lời: a) $a^4-4a^3+8a^2-16a+16$

$=a^4-4a^3+4a^2+4a^2-16a+16$

$=\left(a^4-4a^3+4a^2\right)+\left(4a^2-16a+16\right)$

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

$=a^2\left(a^2-2.a.2+2^2\right)+4\left(a^2-2.a.2+2^2\right)$

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

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

Hàn Vũ · Answer

b)

x3-3x2-7x-15

= x3-5x2+2x2-10x+3x-15

= x2(x-5) + 2x(x-5) + 3(x-5)

= (x-5)(x2+2x+3)Câu trả lời: b)

x3-3x2-7x-15

= x3-5x2+2x2-10x+3x-15

= x2(x-5) + 2x(x-5) + 3(x-5)

= (x-5)(x2+2x+3)