Special Cases and Grouping

There are three forms of quadratic functions we are going to factor. Standard form (like we’ve been doing) ax2 + bx + c Special Cases Factoring by Grouping

There are two types of special cases: Perfect Square Trinomial Difference of Squares

Perfect Square Trinomial Factor the following trinomial: What do you notice about the factors?

Perfect Square Trinomial When the factors of a trinomial are “twins,” we can rewrite them with an exponent! Just like (x)(x) = x2, (2x-3)(2x-3) = (2x-3)2

Try it! Factor! x2 + 20x + 100 9v2 + 12v + 4 p2 – 14p + 49

Difference of Squares What’s a square number? What does “difference” mean in math?

Quick! Find the square numbers!

What ARE the perfect squares? List them out!

Difference of Squares So is 4! Look! 16x2 is a perfect square! And, look! We’re finding the difference! There’s a special formula we can use so we don’t have to do any work. Awesome.

Difference of Squares Formula Try it! x2 – 64 2) 4w2 – 49

Sometimes you have to take out a GCF first! 8y2 – 50 2) 3c2 – 75 3) 28k2 – 7

Factoring By Grouping You’ve seen this already, but sometimes quadratic expressions are given to us with the middle term already split. You can just factor it normally from there.

Try it! xy + 5x + y2 + 5y 2bc + 14b + c + 7 3) 18x3 – 2x2 + 27x – 3

Quick Recap YES NO Okay, now what? YES NO Is the quadratic a difference of squares? Use the difference of squares formula. Factor normally. Are the factors twins? Rewrite them with an exponent. Leave them! YES NO Okay, now what? YES NO

Mix and Match – Factor 2v2 – 12v + 10 2) k2 – 16k + 64 6v3 – 16v2 +21v – 56 4) 63n3 + 54n2 -105n – 90 5) 18k2 – 12k – 6 6) 49m2 - 36