4.3 Solve x2 + bx + c = 0 by Factoring
To factor x2 + bx + c, find factors of c that add up
to b.
Examples: Factor. If the expression cannot be
factored, say "does not factor."
1.) x2 + 4x + 3
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2.) x2 - 9x + 20
3.) x2 + 3x - 12
4.) x2 - 7x + 10
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5.) x2 - 4x - 12
6.) m2 + 8m - 65
7.) p2 + 8p + 16
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Difference of Two Squares
a2 - b2 = (a + b)(a - b)
Examples: Factor.
1.) x2 - 4
2.) a2 - 81
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3.) 100 - x2
4.) x4 - 16
5.) 16x2 - 1
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Zero Product Property
If ab = 0, then a = 0 or b = 0 (or both).
STEPS to solving:
1.) Set equation equal to 0. Keep the squared term positive.
2.) Factor.
3.) Set each factor to 0 and solve.
Examples: Solve.
1.) x2 - 8x + 12 = 0
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2.) w2 - 16w = -48
3.) -3y + 28 = y2
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4.3 ICE
Factor:
1.) x2 + 15x + 56
2.) x2 - 4x - 12
3.) x2 - 11x + 28
Solve:
4.) x2 - 49 = 0
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