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