# Is it possible to factor y= 16x^2 -24x + 9 ? If so, what are the factors?

##### 1 Answer
Jan 11, 2016

$\left(4 x - 3\right) \left(4 x - 3\right)$

#### Explanation:

It is a good idea to try integer coefficients in the factors, since the function itself has all integer coefficients. Since $9 = {3}^{2}$ and the middle term is negative, it's good to check out factors of the form (ax-3)(bx-3), for some coefficients a and b. Since $a x$ times $b x$ must give $16 {x}^{2}$, and $16 = {2}^{4}$, the coefficients a and b must be powers of 2. Trying possibilities, we see it works for a=4 and b=4. That is, for this choice of powers of 2, we get the middle term, namely -24x.