factoring special polynomials
TRANSCRIPT
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 𝑎𝑥2 + 𝑏𝑥 + 𝑐
The first and last terms (𝑎 and 𝑐 ) are both perfect squares
The middle term (𝑏) is equal to 2√𝑎𝑐 1. Factor each trinomial using decomposition. Verify by multiplying/expanding the factors.
a) 36𝑥2 + 12𝑥 + 1 b) 4𝑥2 − 12𝑥 + 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 (√1𝑠𝑡 𝑡𝑒𝑟𝑚 ± √𝑙𝑎𝑠𝑡 𝑡𝑒𝑟𝑚)2
Factor: a) 36𝑥2 + 12𝑥 + 1 b) 4𝑥2 − 12𝑥 + 9
c) 9𝑥2 − 24𝑥 + 16 d) 16 − 56𝑥 + 49𝑥2
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 “O & I” terms will combine to give you middle term
a) 5𝑐2 − 13𝑐𝑑 + 6𝑑2 b) 3𝑝2 − 5𝑝𝑞 − 2𝑞2
Math 10 Unit 3: Factoring (Day 8)
c) 2𝑎2 − 7𝑎𝑏 + 3𝑏2 d) 10𝑐2 − 𝑐𝑑 − 2𝑑2
Factoring a Difference of Squares
Recognizing a difference of squares (𝑥2 − 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 (𝑥2 − 9) = (𝑥 + 3)(𝑥 − 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) 81𝑚2 − 49 b) 162𝑣4 − 2𝑤4
c) 25 − 36𝑥2 d) 5𝑥4 − 80𝑦4 Homework:
2.4 # 9a-d 2.6 # 1-3, 4odd, 5a-l, 6-7odd, 8ab, 9cg