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Math 10 Name: Unit 1: Factoring (Day 8)
Factoring Special Polynomials
Learning Intention(s):
Factor Perfect Square Trinomials, trinomials with 2 variables, and Difference of Squares binomials
Factoring a Perfect Square Trinomial How to identify a perfect square trinomial ๐๐ฅ2 + ๐๐ฅ + ๐
The first and last terms (๐ and ๐ ) are both perfect squares
The middle term (๐) is equal to 2โ๐๐ 1. Factor each trinomial using decomposition. Verify by multiplying/expanding the factors.
a) 36๐ฅ2 + 12๐ฅ + 1 b) 4๐ฅ2 โ 12๐ฅ + 9
Short cut for perfect square trinomials:
Make sure trinomial is in order of descending degree
Set up one set of brackets
Put the square root of the first term at the front of the bracket
Use the sign (+/-) from the middle term
Put the square root of the last term at the end of each bracket
Square the bracket (โ1๐ ๐ก ๐ก๐๐๐ ยฑ โ๐๐๐ ๐ก ๐ก๐๐๐)2
Factor: a) 36๐ฅ2 + 12๐ฅ + 1 b) 4๐ฅ2 โ 12๐ฅ + 9
c) 9๐ฅ2 โ 24๐ฅ + 16 d) 16 โ 56๐ฅ + 49๐ฅ2
Factoring Trinomials with Two Variables Factor each trinomial. Verify by multiplying the factors.
Solve the same way as previous trinomials except: o First variable will be in front of each bracket o Last variable will be at end of each bracket o The โO & Iโ terms will combine to give you middle term
a) 5๐2 โ 13๐๐ + 6๐2 b) 3๐2 โ 5๐๐ โ 2๐2
Math 10 Unit 3: Factoring (Day 8)
c) 2๐2 โ 7๐๐ + 3๐2 d) 10๐2 โ ๐๐ โ 2๐2
Factoring a Difference of Squares
Recognizing a difference of squares (๐ฅ2 โ 9)
First and last term are perfect squares
It is a binomial
Terms are separated by a minus sign
How to factor a difference of squares (๐ฅ2 โ 9) = (๐ฅ + 3)(๐ฅ โ 3)
Set up two sets of brackets
Find the square root of each term
Put them in brackets: one with a + and one with a - Factor each binomial:
a) 81๐2 โ 49 b) 162๐ฃ4 โ 2๐ค4
c) 25 โ 36๐ฅ2 d) 5๐ฅ4 โ 80๐ฆ4 Homework:
2.4 # 9a-d 2.6 # 1-3, 4odd, 5a-l, 6-7odd, 8ab, 9cg