Question

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

Answer 1

`(4x-3)(4x-3)`

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 `ax` times `bx` must give `16x^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.