8-5 Factoring Using the distributive property

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Presentation transcript:

8-5 Factoring Using the distributive property Goals: Use the distributive property to factor a polynomial. Solve polynomial equations by factoring. Eligible Content: A1.1.1.5.2

Vocabulary Monomial – a polynomial that only has one term. Greatest Common Factor – biggest term that all terms are divisible by.

The Greatest Common Factor The GCF is the biggest number the coefficients are divisible by the variable with the smallest exponent.

Find the GCF 5x2 , 15x3 , 35x 5, 15 and 35 are all divisible by 5 x2, x3 , and x are all divisible by x GCF is 5x

Examples Find the GCF. 2x2 and 16x3 32x5, 48x2, 24x3 45x4, 18x, 27x3 4a2b, 8ab2, 2ab 12x3y2, 18x4y3, 9x2y2 2x2 8x2 9x 2ab 3x2y2

factoring using the distributive Property Divide the polynomial by the GCF Remember: when dividing variables you should subtract the exponents!!!! Factor the remaining polynomial if possible.

Factor completely: 6x3 – 36x2 + 48x GCF = 6x 6x3 – 36x2 + 48x 6x 6x 6x 6x( ) 6x( )( ) x2 – 6x + 8 x – 2 x – 4

Examples 14x4y3 – 21x2y 2x3y2 + 8x 4x3 + 20x2 + 24x 45x4 – 20x2 2x(x2y2 + 4) 4x(x + 2)(x + 3) 5x2(3x + 2)(3x – 2) 5x2(x + 3)(x – 6)

Use the Distributive Property to factor the polynomial 3x2y + 12xy2. A. 3xy(x + 4y) B. 3(x2y + 4xy2) C. 3x(xy + 4y2) D. xy(3x + 2y)

Use the Distributive Property to factor the polynomial 3ab2 + 15a2b2 + 27ab3. A. 3(ab2 + 5a2b2 + 9ab3) B. 3ab(b + 5ab + 9b2) C. ab(b + 5ab + 9b2) D. 3ab2(1 + 5a + 9b)

Practice Worksheet – 8-5 Factoring Using the Distributive Property”

Solve the Equations 8x3 – 18x = 0 2x3 – 10x2 + 8x = 0 x = 0, 1.5 or -1.5 x = 0, 1 or 4

Homework Page 497-498 #1-4, 15-20