Question

Phân tích đa thức thành nhân tử

a.(x-1)(x-2)(x+7)(x+8)+8

b.(x²+3x+2)(x²+7x+12)+1

c.a(x²+1)-x(a²+1)

d.(a+b+c)(ab+bc+ca)-abc

e.a³-b³+c³+3abc

Answer 1

a) \(\left(x-1\right)\left(x-2\right)\left(x+7\right)\left(x+8\right)+8\)

\(\Leftrightarrow[\left(x-1\right)\left(x+7\right)][\left(x-2\right)\left(x+8\right)]+8\)

\(\Leftrightarrow\left(x^2+6x-7\right)\left(x^2+6x-16\right)\)+8

Đặt \(x^2+6x-7=a\)

\(\Rightarrow a\left(a-9\right)+8\)\(\)

\(\Leftrightarrow a^2-a-8a+8\)

\(\Leftrightarrow a\left(a-1\right)-8\left(a-1\right)\)

\(\Leftrightarrow\left(a-1\right)\left(a-8\right)\)

\(\Leftrightarrow\left(x^2+6x-8\right)\left(x^2+6x-15\right)\)

Chúc bạn học tốt !!