MPM2D1 Date: _______________

Day 3: Common Factoring Chapter 5: Quadratic Expressions

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Warm-Up: The area of a park is given by the expression 16x2 - 4x. If the length is given by

the expression 4x, what is an expression for the width?

So…what is a “Factor”? Factors are the numbers we multiply together to get another number:

What is the Greatest Common Factor (GCF) ? It is the highest number that divides exactly into two or more numbers.

Greatest Common Factor of 12 and 16

Find all the Factors of each number,

Circle the Common factors,

Choose the Greatest of those

Greatest Common Factor of 24x3y5z and 36x6y4

Find the GCF of the coefficients,

Find the GCF of the variables,

Multiply both terms to get your GCF.

Factors of 24:

Factors of 36:

The GCF is _____

Recall: A = L × W

MPM2D1 Date: _______________

Day 3: Common Factoring Chapter 5: Quadratic Expressions

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Ex1. Consider: 45x5y4z3 and 15x6y4z2

The GCF is __________

HOW TO COMMON FACTOR?

Ex2: Factor 15x2 + 10x (GCF = ___________)

Ex3: Factor -16x4 – 24x3 + 8x2 (GCF = ___________)

Ex4: Factor 9x2 + 6x + 15 (GCF = ___________)

COMMON FACTORING BY GROUPING If there are 4 terms, you may be able to common factor them in pairs.

Ex5: Factor 4x3 + 20x2 + 5x + 25

Common factor the first 2 and

the second 2 terms in pairs

The 2 binomials in brackets

should be equal!

Common factor the binomial

in brackets

MPM2D1 Date: _______________

Day 3: Common Factoring Chapter 5: Quadratic Expressions

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Ex6: Factor 14m3 – 21m2 + 12m – 18

Ex7: Factor 2k3 – 7k2 – 4k +14

Ex8: Factor 14v3 – 2v2 + 7v – 1