Factoring - Algebra 1+

What is the first step of factoring?

Always look for a GCF, and if there is one factor it out

What is the 2nd step of factoring?

Check what type of polynomial we have: binomial, trinomial (ax²+bx+c), 4 term polynomial

What do we do if its a binomial?

Check if its a difference of squares: yes (factor it out), no (your done!)

What to do if we have a trinomial?

Rewrite as a polynomial with 4 terms by spilting the middle into 2 numbers that multiply to AC and add to B

What to do if we have a 4 term polynomial?

Factor by grouping or area model

What does factoring mean?

To undistribute, to factor, start by taking out the GCF

How do you use an area model?

Find GCF of any row/ column, turn it back into multiplication

What are the steps of factoring with trinomials?

1. Identify our ABC terms

2. Find terms that multiply to AC and add to B

3. Plug into the preferred method

4. Check your final answer by multiplying diagonally (area model) / multiply out (grouping)

What is the formula for a difference of squares?

(x²-y²) = (x+y) (x-y) (add THEN subtract)

What are 3 criteria to look out for when factoring a difference of squares?

1. Make sure we’re working with a binomial (2 terms)

2. We’re subtracting 2 terms

3. Make sure our 1st and 2nd numbers are perfect squares (can be squarerooted)

What are patterns with difference of squares?

Middle terms canceled out, the 1st and last terms are the same, the 1st last term are positive, the 2nd last term is negative

• Ex.= (x+3)(x-3) = x²- 9

• (y²+4)(y²-4) = y^4-16