Factoring — Break It Apart

Factoring is faster than the quadratic formula when it works.

GCF first: Always pull out the greatest common factor.

6x2 + 12x = 6x(x + 2)

Standard trinomial: x2 + bx + c

Find two numbers that multiply to c and add to b.

x2 + 7x + 12 = (x + 3)(x + 4) because 3 x 4 = 12 and 3 + 4 = 7

Difference of squares: a2 - b2 = (a + b)(a - b)

x2 - 49 = (x + 7)(x - 7)

Perfect square trinomial:

x2 + 6x + 9 = (x + 3)2

x2 - 10x + 25 = (x - 5)2

SAT tip: If you can't factor in 30 seconds, use the quadratic formula or plug it into Desmos. Don't waste time.

Reference:

Wikipedia: Factorization

https://en.wikipedia.org/wiki/Factorization