Factoring Polynomials Review ► (9.5) Factor x² + bx + c ► (9.6) Factor ax² + bx + c ► (9.7) Factor special products x² – 7x – 30 (x – 10)(x + 3) 3z² +

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Presentation transcript:

Factoring Polynomials Review ► (9.5) Factor x² + bx + c ► (9.6) Factor ax² + bx + c ► (9.7) Factor special products x² – 7x – 30 (x – 10)(x + 3) 3z² + z – 14 (3z + 7)(z – 2) 9z² – 36z + 36 (3z – 6)² 72z² – 98 2(6z – 7)(6z + 7) Perfect square trinomial Difference of two squares

►F►F►F►Factor out a common binomial- 2222x(x + 4) – 3(x + 4) ►F►F►F►Factor by grouping- xxxx³ + 3x² + 5x + 15 Section 9.8 “Factor Polynomials Completely”

2x(x + 4) – 3(x + 4) Factor out a common binomial Factor out the common binomial 2x(x + 4) – 3(x + 4) = (x + 4) (2x – 3) (2x – 3) 4x²(x – 3) + 5(x – 3) Factor out the common binomial 4x²(x – 3) + 5(x – 3) = (x – 3) (4x² + 5) (4x² + 5)

7y(y – 2) + 3(2 – y) Factor out a common binomial The binomials y – 2 and 2 – y are opposites. Factor out -1 from 3(2 – y) to obtain -3(y – 2). Factor out the common binomial 7y(y – 2) – 3(y – 2) = (y – 2) (7y – 3) (7y – 3) 7y(y – 2) – 3(y – 2)

2y²(y – 4) – 6(4 – y) Factor out a common binomial…Try It Out The binomials y – 4 and 4 – y are opposites. Factor out -1 from -6(4 – y) to obtain 6(y – 4). Factor out the common binomial 2y²(y – 4) + 6(y – 4) = (y – 4) (2y² + 6) (2y² + 6) 2y²(y – 4) + 6(y – 4)

x³ + 3x² + 5x + 15 Factor by grouping Group terms into binomials and look to factor out a common binomial. Factor out each group x²(x + 3) + 5(x + 3) = (x + 3) (x² + 5) (x² + 5) (x³ + 3x²) + (5x + 15) (x + 3) x² + 5 Factor out the common binomial

x³ – 6 + 2x – 3x² Factor by grouping…Try It Out Group terms into binomials and look to factor out a common binomial. Factor out each group x²(x – 3) + 2(x – 3) = (x – 3) (x² + 2) (x² + 2) (x³ – 3x²) + (2x – 6) (x – 3) x² + 2 Factor out the common binomial Reorder polynomial with degree of powers decreasing from left to right. x³ – 3x² + 2x – 6

Factoring Polynomials Completely ►(►(►(►(1) Factor out greatest common monomial factor. ►(►(►(►(2) Look for difference of two squares or perfect square trinomial. ►(►(►(►(3) Factor a trinomial of the form ax² + bx + c into binomial factors. ►(►(►(►(4) Factor a polynomial with four terms by grouping. 3x² + 6x= 3x(x + 2) x² + 4x + 4= (x + 2)(x + 2) 16x² – 49= (4x + 7)(4x – 7) 3x² – 5x – 2= (3x + 1)(x – 2) -4x² + x + x³ - 4= (x² + 1)(x – 4)