5-4 Factoring Quadratic
Expressions
Objectives:
 Factor a difference of squares.
 Factor quadratics in the form
 Factor out the GCF.
 Factor quadratics with a GCF.
Definitions
Greatest Common Factor – the biggest
number that will divide all terms evenly. If
there are variables, the lower exponent is in
the GCF.
examples:
Find the GCF
1) 9, 12
Class Work 5-4
Find the GCF:
1) 18, 20
2) 12, 24, 30
3) 4x, 20x
4) x2, 6x
5) 27x2, 36
6) 5x2, 6xy
7) 3y, 8x
8) 2x3, 3x2
9) 36a4, 72a2
Factor out the GCF
1) x2 – 9x
2) 3x2 – 18x
3) 12x3 – 18x2
4) 2x2 + 4x + 10
Recognizing a Difference of Squares
There are ONLY two terms in the problem.
It MUST be a minus sign in the middle.
BOTH terms are perfect squares
This is an example of a difference of squares
4x2 - 25
Perfect Squares
9 is a perfect square because 3 x 3 = 9
36 is a perfect square because 6 x 6 = 36
81 is a perfect square because 9 x 9 = 81
12 is NOT a perfect square because there is
no number times itself that will give you 12.
Circle the Perfect Squares
16, 36, 20, 121, 144, 60, 50, 4, 225
9x2, 10x2, 81x3, 100x2, 44x2, 1000x4, 30x2
Class Work 5-4
Factor:
1) x2 – 4
2) x2 - 81
3) 4x2 – x
4) 25x2 – 9
5) 100x4 – 49
6) 49x2 + 1
8) 4x2 + 25
9) 121x2 – 81y2
Factoring Polynomials in the Form
ax2 + bx - c
Factor:
1) x2 – 14x – 32
2) x2 + 13x + 22
3) x2 + 15xy + 14y2
4) x2 + 7x – 12
5) 6x2 + 13x + 2
6) 10x2 – 13x + 4
Factoring Problems with a GCF
1) 4x2 – 16x – 48
2) 6x2 – 42x + 36
3) 2x2 + 46x – 100
4) x3 – 4x
5) 6x2 + 13x + 2
6) 6x2 – 6x - 72