Question

Phân tích đa thức thành nhân tử:

a. \(2x^3-x^2+5x+3\)

b. \(x^3+5x^2+8x+4\)

c. (x + 2)(x + 3)(x + 4)(x + 5) - 24

d. \(4x^4+1\)

e. \(x^4-7x^3+14x^2-7x+1\)

Answer 1

a: \(=2x^3+x^2-2x^2-x+6x+3\)

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

b: \(=x^3+x^2+4x^2+4x+4x+4\)

\(=\left(x+1\right)\left(x^2+4x+4\right)\)

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

c: \(=\left(x^2+7x+12\right)\left(x^2+7x+10\right)-24\)

\(=\left(x^2+7x\right)^2+22\left(x^2+7x\right)+96\)

\(=\left(x^2+7x+6\right)\left(x^2+7x+16\right)\)

\(=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)