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8.3 – Factoring Trinomials: x 2 + bx + c
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8.3 – Factoring Trinomials: x2 + bx + c
Recall: Simplify (x + 2)(x + 3).
Recall: Simplify (x + 2)(x + 3).
(x · x)
Recall: Simplify (x + 2)(x + 3).
(x · x) + (x · 3)
Recall: Simplify (x + 2)(x + 3).
(x · x) + (x · 3) + (2 · x)
Recall: Simplify (x + 2)(x + 3).
(x · x) + (x · 3) + (2 · x) + (2 · 3)
Recall: Simplify (x + 2)(x + 3).
(x · x) + (x · 3) + (2 · x) + (2 · 3)x2 + 3x + 2x + 6
Recall: Simplify (x + 2)(x + 3).
(x · x) + (x · 3) + (2 · x) + (2 · 3)x2 + 3x + 2x + 6x2 + (3 + 2)x + 6
Recall: Simplify (x + 2)(x + 3).
(x · x) + (x · 3) + (2 · x) + (2 · 3)x2 + 3x + 2x + 6x2 + (3 + 2)x + 6 x2 + 5x + 6
Recall: Simplify (x + 2)(x + 3).
(x · x) + (x · 3) + (2 · x) + (2 · 3)x2 + 3x + 2x + 6x2 + (3 + 2)x + 6 x2 + 5x + 6
Ex. 1 Factor x2 + 5x + 6.
Recall: Simplify (x + 2)(x + 3).
(x · x) + (x · 3) + (2 · x) + (2 · 3)x2 + 3x + 2x + 6x2 + (3 + 2)x + 6 x2 + 5x + 6
Ex. 1 Factor x2 + 5x + 6. (x )(x )
Recall: Simplify (x + 2)(x + 3).
(x · x) + (x · 3) + (2 · x) + (2 · 3)x2 + 3x + 2x + 6x2 + (3 + 2)x + 6 x2 + 5x + 6
Ex. 1 Factor x2 + 5x + 6. (x )(x )
ax2 + bx + c = (x + m)(x + n) such that m + n = b and mn = c
Ex. 2 Factor x2 + 6x + 8.
Ex. 2 Factor x2 + 6x + 8.
x2 + 6x + 8 = (x )(x )
Ex. 2 Factor x2 + 6x + 8.
x2 + 6x + 8 = (x )(x )
= (x + 2)(x + 4)
Ex. 2 Factor x2 + 6x + 8.
x2 + 6x + 8 = (x )(x )
= (x + 2)(x + 4)
Ex. 3 Factor x2 – 10x + 16.
Ex. 2 Factor x2 + 6x + 8.
x2 + 6x + 8 = (x )(x )
= (x + 2)(x + 4)
Ex. 3 Factor x2 – 10x + 16.
x2 – 10x + 16 = (x )(x)
Ex. 2 Factor x2 + 6x + 8.
x2 + 6x + 8 = (x )(x )
= (x + 2)(x + 4)
Ex. 3 Factor x2 – 10x + 16.
x2 – 10x + 16 = (x )(x)
= (x – 2)(x – 8)
Ex. 2 Factor x2 + 6x + 8.
x2 + 6x + 8 = (x )(x )
= (x + 2)(x + 4)
Ex. 3 Factor x2 – 10x + 16.
x2 – 10x + 16 = (x )(x )
= (x – 2)(x – 8)
Ex. 4 Factor x2 + x – 12.
Ex. 2 Factor x2 + 6x + 8. x2 + 6x + 8 = (x )(x )
= (x + 2)(x + 4)
Ex. 3 Factor x2 – 10x + 16. x2 – 10x + 16 = (x )(x )
= (x – 2)(x – 8)
Ex. 4 Factor x2 + x – 12. x2 + x – 12 = (x )(x )
Ex. 2 Factor x2 + 6x + 8. x2 + 6x + 8 = (x )(x )
= (x + 2)(x + 4)
Ex. 3 Factor x2 – 10x + 16. x2 – 10x + 16 = (x )(x )
= (x – 2)(x – 8)
Ex. 4 Factor x2 + x – 12. x2 + x – 12 = (x )(x )
= (x + 4)(x – 3)
Ex. 5 Factor x2 – 7x – 18.
Ex. 5 Factor x2 – 7x – 18.
x2 – 7x – 18 = (x )(x )
Ex. 5 Factor x2 – 7x – 18.
x2 – 7x – 18 = (x )(x )
= (x + 2)(x – 9)
Ex. 5 Factor x2 – 7x – 18.
x2 – 7x – 18 = (x )(x )
= (x + 2)(x – 9)
Ex. 6 Solve x2 + 5x = 6.
Ex. 5 Factor x2 – 7x – 18.
x2 – 7x – 18 = (x )(x )
= (x + 2)(x – 9)
Ex. 6 Solve x2 + 5x = 6.
x2 + 5x = 6
-6 -6
Ex. 5 Factor x2 – 7x – 18.
x2 – 7x – 18 = (x )(x )
= (x + 2)(x – 9)
Ex. 6 Solve x2 + 5x = 6.
x2 + 5x = 6
-6 -6
x2 + 5x – 6 = 0
Ex. 5 Factor x2 – 7x – 18.x2 – 7x – 18 = (x )(x )
= (x + 2)(x – 9)
Ex. 6 Solve x2 + 5x = 6. x2 + 5x = 6 -6 -6 x2 + 5x – 6 = 0 (x )(x ) = 0
Ex. 5 Factor x2 – 7x – 18.
x2 – 7x – 18 = (x )(x )
= (x + 2)(x – 9)
Ex. 6 Solve x2 + 5x = 6.
x2 + 5x = 6
-6 -6
x2 + 5x – 6 = 0
(x )(x ) = 0
(x – 1)(x + 6) = 0
Ex. 5 Factor x2 – 7x – 18.x2 – 7x – 18 = (x )(x )
= (x + 2)(x – 9)
Ex. 6 Solve x2 + 5x = 6. x2 + 5x = 6 -6 -6 x2 + 5x – 6 = 0 (x )(x ) = 0(x – 1)(x + 6) = 0
x – 1 = 0 x + 6 = 0
Ex. 5 Factor x2 – 7x – 18.x2 – 7x – 18 = (x )(x )
= (x + 2)(x – 9)
Ex. 6 Solve x2 + 5x = 6. x2 + 5x = 6 -6 -6 x2 + 5x – 6 = 0 (x )(x ) = 0(x – 1)(x + 6) = 0
x – 1 = 0 x + 6 = 0 x = 1 x= -6
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