factor the polynomial x^3 + 4x^2 + 5x + 2

Question

x^3 + 4x^2 + 5x + 2.

Answer 1

Recall the formula (a+b)^2 = a^2+2ab+b^2.

Given polynomial x^3+4x^2+5x+2

= x(x^2+4x+5)+2

= x(x^2+4x+4+1)+2

= x(x^2+4x+4)+x+2

= x(x+2)^2+(x+2)

Take common out (x+2) from above expression.

= (x+2)[x(x+2)+1]

= (x+2)[x^2+2x+1]

= (x+2)(x+1)^2

Factoring of given polynomial x^3+4x^2+5x+2 = (x+2)(x+1)(x+1).