Factoring Quadratic Expressions Section 5.4 Factoring Quadratic Expressions

Finding Common and Binomial Factors Definition 1: Factoring is rewriting an expression as the product of its factors. Definition 2: The greatest common factor (GCF) is a common factor of the terms of the expression.

Examples 1 – 3 Factor each expression. 4 𝑥 2 +20𝑥−12 9 𝑛 2 −24𝑛 9 𝑥 2 +3𝑥−18

Examples 4 & 5 Factor each expression. 7 𝑝 2 +21 4 𝑤 2 +2𝑤

Examples 6 & 7 Factor each expression. 𝑥 2 +8𝑥+7 𝑥 2 +6𝑥+8

Examples 8 & 9 Factor each expression. 𝑥 2 +12𝑥+32 𝑥 2 +14𝑥+40

TOTD Factor each expression. 15x² + 25x + 100 8m² + 4m

Examples 10 – 11 Factor each expression. 𝑥 2 −17𝑥+72 𝑥 2 −6𝑥+8

Examples 12 – 13 Factor each expression. 𝑥 2 −7𝑥+12 𝑥 2 −11𝑥+24

Examples 14 – 15 Factor each expression. 𝑥 2 −𝑥−12 𝑥 2 −14𝑥−32

Examples 16 – 17 Factor each expression. 𝑥 2 +3𝑥−10 𝑥 2 +4𝑥−5

Examples 18 – 19 Factor each expression. 3 𝑥 2 −16𝑥+5 2 𝑥 2 +11𝑥+12

Examples 20 – 21 Factor each expression. 4 𝑥 2 +7𝑥+3 2 𝑥 2 −7𝑥+6

TOTD Factor. x² + 10x + 24 x² - 14x + 33

Examples 22 – 23 Factor each expression. 4 𝑥 2 −4𝑥−15 2 𝑥 2 +7𝑥−9

Examples 24 – 25 Factor each expression. 3 𝑥 2 −16𝑥−12 4 𝑥 2 +5𝑥−6

Factoring Special Expressions Definition 3: A perfect square trinomial is the product you obtain when you square a binomial.

Examples 26 – 27 Factor each expression. 9 𝑥 2 −42𝑥+49 64 𝑥 2 −16𝑥+1

Examples 28 – 29 Factor each expression. 4 𝑥 2 +12𝑥+9 25 𝑥 2 +90𝑥+81

Difference of Squares An expression of the form a2 – b2 is defined as the difference of two squares.

Examples 30 & 31 Factor each expression. 𝑥 2 −64 4 𝑎 2 −49

TOTD Factor each expression completely. m² + 11m + 18 3x² + 5x - 50