Factoring Special Cases. Factoring by Grouping. What you’ll learn To factor perfect square...
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Transcript of Factoring Special Cases. Factoring by Grouping. What you’ll learn To factor perfect square...
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