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Lesson 10.5: Factoring x2 + bx + c Recall: Using Foil (x + 3)(x + 7) = ? x2 + 10x + 21 How can we go backward? Factor x2 + 10x + 21 (x + 3)(x + 7)

“Grind it out “ method of factoring Factoring x2 + bx + c **** Looking for factors of “c” whose sum is “b” - Factors are two binomials - the first term of each binomial = square root of first term of trinomial - second terms of binomials = factors of “c”, whose sum is “b”

Factor completely. x2 + 8x + 15 2) x2 + 11x + 10 ( )( ) (x + 10)(x + 1) x x + 3 + 5 x2 – 17x + 60 (x – 12) ( x – 5) x2 – 9x + 20 (x – 4)(x – 5)

Factor completely. x2 – 8x – 9 (x – 9)( x + 1) x2 + 2x – 48 (x + 8)(x – 6)

When factoring x2 + bx + c IF b and c are positive, use positive factors of c IF b is negative and c is positive, use negative factors of c. IF c is negative, use one positive factor of c and one negative factor of c.

Factoring Steps: 1) Look for GCMF 2) Look for Diff. Of two squares 3) Look for Trinomial Square 4) Grind it out

x2 – 5x = 24 x2 – 5x – 24 = 24 – 24 x2 – 5 x – 24 = 0 (x – 8)(x + 3) = 0 x – 8 = 0 or x + 3 = 0 x – 8 + 8 = 0 + 8 x = 8 x + 3 – 3 = 0 – 3 x = - 3 x = {-3, 8}

Discriminant of a quadratic expression: b2 – 4ac Quadratic Expression is factorable if the discriminant is a perfect square Expression is PRIME if the discriminant is NOT a perfect square Ex. Determine if factorable or prime x2 + 6x – 7 2) x2 + 6x – 8 62 – 4(1)(7) 36 – 28 8 PRIME 62 – 4(1)(8) 36 -32 4 Factorable

Homework : p.607, #12-46 evens

Factor: x2 – 14x + 24 (x – 12)(x – 2) x2 + 20x + 36 (x + 18)(x + 2)

Solve. x2 + 11x + 18 = 0 (x + 9)(x + 2) = 0 x + 9 = 0 or x + 2 = 0 x + 9 – 9 = 0 – 9 x = -9 x + 2 – 2 = 0 – 2 x = -2 x = {-2, -9}