Factoring

What do you always do first?

GCF

If there are 2 terms what do you look for?

Difference of 2 Squares

If there is a difference of two squares what formula do you use?

(a+b)(a-b)

What is the difference of 2 squares?

a² - b² =

If it is not a difference of two squares or sum/difference of cubes, what is it?

sum of squares (prime)

If it is not a difference or sum of two squares what is it?

Sum/difference of cubes

What are the 2 formulas for the sum of cubes?

a³+b³=
(a+b)(a²-ab+b²)=

What are the 2 formulas for the difference of cubes?

a³-b³=
(a-b)(a²+ab+b²)=

If there are 3 terms what do you look for?

Perfect square trinomials

How do you look for perfect square trinomials if the first coefficient is 1?

Half the middle term and square it, it should be equal to the last term

How do you look for perfect square trinomials if the first coefficient isn’t 1?

Square root the 1st and last term and multiply then together, it should equal the middle term

If it isn’t a perfect square trinomial and the leading coefficient isn’t 1 what do you do?

Factor using the ac method

How do you use the AC method

Multiply the first with the last coefficient and figure out what multiplies to that number and adds to the middle term. Take those 2 numbers and factor using grouping.

If it isn’t a perfect square trinomial and the leading coefficient is 1 what do you do?

X²+bx+c=
(x+p)(x+q)

when b=p+q and c=p*q

What formula do you use if it is a perfect square trinomial?

a²±2ab+b²=
(a±b)²

How do you use the perfect square trinomial formula

square the first and last term. for the middle, multiply the 2 numbers ((a±b)) inside the parentheses and *2x

what do you do if there is 4+ factors

factor by grouping