Question

Factor completely 2x^2 +9x +9

Answer 1

(x + 3)*(x + 1.5)

Explanation:

Factoring a second degree polynomial:

Suppose we have a second degree polynomial in the following format:

ax² + bx + c = 0

It's factorization is given by:

a(x - x')(x - x'')

In which x' and x'' are the roots of the polynomial.

Finding the roots of a polynomial:

The roots of the polynomial above are given by:

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

In this question:

The polynomial is: 2x² + 9x + 9

So a = 2, b = 9, c = 9.

The roots are:

`x=\frac{-9\pm\sqrt[]{9^2-4\ast2\ast9}}{2\ast2}=(-9\pm3)/(4)`
`x^{^(\prime)}=(-9-3)/(4)=(-12)/(4)=-3`
`x^{^(\prime)^(\prime)}=(-9+3)/(4)=(-6)/(4)=-1.5`

So, the factorization is:

(x - (-3))*(x - (-1.5)) = (x + 3)*(x + 1.5)