How do you factor the expression #9x^2+9x+2#?

Question

Savannah Anderson · Accepted Answer

You look for its roots with the quadratic formula.

We first need #Delta = b^2 - 4ac = 9#. So there are two real roots. By the quadratic formula, a root is given by the expression #(-b +- sqrtDelta)/2a#. We apply it here. #x_1 = (-9 - 3)/18 = -2/3# and #x_2 = (-9 + 3)/18 = -1/3#. So this polynomial is equal to #9(x + 2/3)(x + 1/3)#.

Eli Assouline · Answer

undefined To factor the expression $9x^2 + 9x + 2$, you can use the quadratic formula or factorization by decomposition method.

Using the quadratic formula, $x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$, where $a = 9$, $b = 9$, and $c = 2$:

$x = \frac{{-9 \pm \sqrt{{9^2 - 4(9)(2)}}}}{{2(9)}}$

$x = \frac{{-9 \pm \sqrt{{81 - 72}}}}{{18}}$

$x = \frac{{-9 \pm \sqrt{9}}}{{18}}$

$x = \frac{{-9 \pm 3}}{{18}}$

This gives us two roots: $x = \frac{{-9 + 3}}{{18}}$ and $x = \frac{{-9 - 3}}{{18}}$, which simplify to $x = \frac{1}{3}$ and $x = -\frac{2}{3}$, respectively.

Therefore, the factored form of $9x^2 + 9x + 2$ is $9(x - \frac{1}{3})(x + \frac{2}{3})$.