First Things First
When factoring, the first step should always be to check for this.
What is GCF.
This is the main goal when factoring by grouping.
What is to find the common binomial factor.
When factoring sums or differences of cubes, this is the tip that helps us keep the signs clean.☺️
What is SOAP.
These two numbers have a product of -21 and a sum of 4.
What are 7 and -3
GCF stand for this.
What is Greatest Common Factor.
The go-to for factoring a 4 term polynomial is this method.
What is factoring by grouping.
If the two groups do not produce the same binomial factor, you should try this.
What is to rearrange the terms and try again.
Factor 100x^2-9
(10x-3)(10x+3)
This is pair of numbers I need to factor 6x^2 +11x +3.
What are 9 and 2.
If the constant term is negative, this must be true about the signs of it's two factors.
What is one must be positive and the other must be negative.
If a trinomial doesn't have a GCF, I should check for this pattern first.
What is a perfect square trinomial pattern.
Factor: x^3+3x^2+2x+6 .
(x+3)(x^2+2)
Factor me completely. 25x^2 -20x+4
(5x-2)^2
Factor x^2+10x-24
(x+12)(x-2)
If factoring a perfect square trinomial, this term dictates when the binomial factor uses addition or subtraction.
What is the middle term.
This is the first move in factoring x^4 -8x^2+16.
What is applying the Perfect Square Trinomial formula.
Factor completely: 2x^3-10x+2x^2-10
2(x^2-5)(x+1)
Factor 125x^3-8
(5x-2)(25x^2+10x+4)
Factor 4x^2-5x-9
(4x-9)(x+1)
If a polynomial's lead term is negative, this is a good strategy.
What is factor out a
-1.
This is the first move in factoring 81x^4-1.
What is applying the difference of two squares formula.
Factor: 9x^3-10+6x^2-15x
(3x+2)(3x^2-5)
Factor 216x^3+343
(6x+7)(36x^2-42x+49)
Factor 12x^2-22x-10 completely.
2(2x-5)(3x+2)
After factoring out a GCF, one should always look for this.
What is whether the remaining polynomial can be factored further.