Question

Factor the polynomial
4x^2 + 12 + 9

Answer 1

The answer is
`(2x+3)^2`.

Explanation:

Multiply the coefficient of the squared term and the constant. Then, find the factors that add up to 12:

`4*9=36\\36:\{1*36,2*18,3*12,4*9,6*6\}\\6+6=12`

Split the middle term:

`4x^2+6x+6x+9`

Factor by grouping:

`[4x^2+6x]+[6x+9]\\2x(2x+3)+3(2x+3)\\(2x+3)(2x+3)\\(2x+3)^2`