Question

How do you factor completely `77x^2+102x+16`?

Answer 1

`(11x + 2)(7x + 8)`

Explanation:

If the factored form of a quadratic is `y = (ax+b)(cx+d)`
the standard form is `acx^2 +(ad+bc)x +bd`
In this example therefore we need to find factors of `77 (ac)` and `16 (bd)` that add to give `102 (ad + bc)`
`77 = 7 * 11` and `16 = 8*2`
`11*8 +7*2 = 88 + 14 = 102`
The result is therefore `(11x + 2)(7x + 8)`