Question

Factorize of the following polynomials:

4x³ + 20x² + 33x + 18 given that 2x + 3 is a factor.

Answer 1

Let ` f(x) = 4x^3 + 20x^2 + 33x+ 18` be the given polynomial.

Therefore (2x + 3)is a factor of the polynomial f(x).

Now,

`f(x)=  2x^2 (2x + 3)+7x(2x + 3) + 6(2x + 3)`

        `=(2x + 3){2x^2 + 4x 3x + 6}`

        `= (2x + 3){2x^2 + 4x + 3x + 6}`

        ` = (2x + 3)(2x + 3)(x + 2)`

Hence (x +2),(2x+3) and (2x + 3 ) are the factors of polynomial f(x).