8.3 – Factoring Trinomials: x 2 + bx + c. Recall: Simplify (x + 2)(x + 3).

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Presentation transcript:

8.3 – Factoring Trinomials: x 2 + bx + c

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) x 2 + 3x + 2x + 6

Recall: Simplify (x + 2)(x + 3). (x · x) + (x · 3) + (2 · x) + (2 · 3) x 2 + 3x + 2x + 6 x 2 + (3 + 2)x + 6

Recall: Simplify (x + 2)(x + 3). (x · x) + (x · 3) + (2 · x) + (2 · 3) x 2 + 3x + 2x + 6 x 2 + (3 + 2)x + 6 x 2 + 5x + 6

Recall: Simplify (x + 2)(x + 3). (x · x) + (x · 3) + (2 · x) + (2 · 3) x 2 + 3x + 2x + 6 x 2 + (3 + 2)x + 6 x 2 + 5x + 6 Ex. 1 Factor x 2 + 5x + 6.

Recall: Simplify (x + 2)(x + 3). (x · x) + (x · 3) + (2 · x) + (2 · 3) x 2 + 3x + 2x + 6 x 2 + (3 + 2)x + 6 x 2 + 5x + 6 Ex. 1 Factor x 2 + 5x + 6. (x )(x)

Recall: Simplify (x + 2)(x + 3). (x · x) + (x · 3) + (2 · x) + (2 · 3) x 2 + 3x + 2x + 6 x 2 + (3 + 2)x + 6 x 2 + 5x + 6 Ex. 1 Factor x 2 + 5x + 6. (x )(x) ax 2 + bx + c = (x + m)(x + n) such that m + n = b and mn = c

Ex. 2 Factor x 2 + 6x + 8.

x 2 + 6x + 8 = (x )(x)

Ex. 2 Factor x 2 + 6x + 8. x 2 + 6x + 8 = (x )(x) = (x + 2)(x + 4)

Ex. 2 Factor x 2 + 6x + 8. x 2 + 6x + 8 = (x )(x) = (x + 2)(x + 4) Ex. 3 Factor x 2 – 10x + 16.

Ex. 2 Factor x 2 + 6x + 8. x 2 + 6x + 8 = (x )(x) = (x + 2)(x + 4) Ex. 3 Factor x 2 – 10x x 2 – 10x + 16 = (x )(x)

Ex. 2 Factor x 2 + 6x + 8. x 2 + 6x + 8 = (x )(x) = (x + 2)(x + 4) Ex. 3 Factor x 2 – 10x x 2 – 10x + 16 = (x )(x) = (x – 2)(x – 8)

Ex. 2 Factor x 2 + 6x + 8. x 2 + 6x + 8 = (x )(x) = (x + 2)(x + 4) Ex. 3 Factor x 2 – 10x x 2 – 10x + 16 = (x )(x) = (x – 2)(x – 8) Ex. 4 Factor x 2 + x – 12.

Ex. 2 Factor x 2 + 6x + 8. x 2 + 6x + 8 = (x )(x) = (x + 2)(x + 4) Ex. 3 Factor x 2 – 10x x 2 – 10x + 16 = (x )(x) = (x – 2)(x – 8) Ex. 4 Factor x 2 + x – 12. x 2 + x – 12 = (x )(x)

Ex. 2 Factor x 2 + 6x + 8. x 2 + 6x + 8 = (x )(x) = (x + 2)(x + 4) Ex. 3 Factor x 2 – 10x x 2 – 10x + 16 = (x )(x) = (x – 2)(x – 8) Ex. 4 Factor x 2 + x – 12. x 2 + x – 12 = (x )(x) = (x + 4)(x – 3)

Ex. 5 Factor x 2 – 7x – 18.

x 2 – 7x – 18 = (x )(x)

Ex. 5 Factor x 2 – 7x – 18. x 2 – 7x – 18 = (x )(x) = (x + 2)(x – 9)

Ex. 5 Factor x 2 – 7x – 18. x 2 – 7x – 18 = (x )(x) = (x + 2)(x – 9) Ex. 6 Solve x 2 + 5x = 6.

Ex. 5 Factor x 2 – 7x – 18. x 2 – 7x – 18 = (x )(x) = (x + 2)(x – 9) Ex. 6 Solve x 2 + 5x = 6. x 2 + 5x =

Ex. 5 Factor x 2 – 7x – 18. x 2 – 7x – 18 = (x )(x) = (x + 2)(x – 9) Ex. 6 Solve x 2 + 5x = 6. x 2 + 5x = x 2 + 5x – 6 = 0

Ex. 5 Factor x 2 – 7x – 18. x 2 – 7x – 18 = (x )(x) = (x + 2)(x – 9) Ex. 6 Solve x 2 + 5x = 6. x 2 + 5x = x 2 + 5x – 6 = 0 (x )(x) = 0

Ex. 5 Factor x 2 – 7x – 18. x 2 – 7x – 18 = (x )(x) = (x + 2)(x – 9) Ex. 6 Solve x 2 + 5x = 6. x 2 + 5x = x 2 + 5x – 6 = 0 (x )(x) = 0 (x – 1)(x + 6) = 0

Ex. 5 Factor x 2 – 7x – 18. x 2 – 7x – 18 = (x )(x) = (x + 2)(x – 9) Ex. 6 Solve x 2 + 5x = 6. x 2 + 5x = x 2 + 5x – 6 = 0 (x )(x) = 0 (x – 1)(x + 6) = 0 x – 1 = 0x + 6 = 0

Ex. 5 Factor x 2 – 7x – 18. x 2 – 7x – 18 = (x )(x) = (x + 2)(x – 9) Ex. 6 Solve x 2 + 5x = 6. x 2 + 5x = x 2 + 5x – 6 = 0 (x )(x) = 0 (x – 1)(x + 6) = 0 x – 1 = 0x + 6 = 0 x = 1 x= -6