Factoring Special Cases. Factoring by Grouping.

What you’ll learn

To factor perfect square trinomials and differences squares.To factor higher degree polynomials by grouping.

Vocabulary

Perfect square trinomial.Difference of two squares.Factoring by grouping.

Note:

Any trinomial of the form or is a perfect square trinomial because it is the result of squaring a binomial.

22 2 baba 22 2 baba

222

222

2

2

bababababa

bababababa

: bandanumberrealanyFor

Here is how to recognize a perfect square trinomial:*the first and last term are perfect squares*the middle term is twice the product of one factorfrom the first term and one factor of the last term.

Problem 1: Factoring a perfect square trinomial.

What is the factored form of?

36122 xx

22 662 xx

Write the last term as a square

Does the middle term equal -2ab?-12x=-2(x)(6)

Write as the square of a binomial.

Your turnWhat is the factored form of each expression?

4914)

96)2

2

xxb

xxa 2

2

7)

3)

xb

xaAnswers:

26x

Take a note: Factoring a Difference of Two Squares.

8864:

b and a numbers real allFor

2

22

xxxExample

bababa

.

Problem 2: What is the factored form of?

624)

6425)

8116)

2

2

2

gc

db

xa 9494 xx

8585 dd

12126146 2 ggg

Take a note: Factoring by grouping is when you group the terms in pairs, factored the GCF from each pair, and looked for a common binomial factor.

Problem 3:

What is the factored form of?

423

4243)2

2

nn

nnna

7452) 2 ttb

234

2324

6324)

2

2

23

qqq

qqqq

qqqqc

3223) 2 hhhd

h18h12h9h6)d

q24q12q8q4)c

35t20t14t8)b

8n2n12n3)a

234

234

23

23

Take a note: When factoring polynomials 1. Factor out the greatest common factor.GCF 2.If the polynomial has two terms or three terms, look for a difference of two squares, a perfect square trinomial, or a pair of binomials factors. 3.If the polynomial has four or more terms, group terms and factor to find common binomial factors. 4. As a final check, make sure there are no common factors other than 1.

Class work odd Homework evenTB pgs 514-515 exercises 9-41 pgs 519-520 exercises 9-40