8-1 and 8-2 Factoring Using the Distributive Property Algebra 1 Glencoe McGraw-HillLinda Stamper.

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Presentation transcript:

8-1 and 8-2 Factoring Using the Distributive Property Algebra 1 Glencoe McGraw-HillLinda Stamper

You have used the distributive property to determine a product – for example: You can also use the distributive property to take the product and return it to factored form – for example: Today you will use the distributive property to factor out constants and or variables that are common terms of a polynomial. A polynomial is prime if it cannot be factored using integer coefficients. To factor a polynomial completely, write it as the product of a monomial and prime factors.

Find the greatest monomial factor. Then factor it out of the expression. Write as prime factors. Circle common primes Find the GMF (multiply the common primes). Use the distributive property to factor out the GMF Check – Multiply the factors together using the distributive property. Whatever is NOT circled goes in parentheses.

Find the greatest monomial factor. Then factor it out of the expression. The problem. Think of the GCF. Use the distributive property to factor out the GCF You are using division when you factor the GCF out of the expression!

Find the greatest monomial factor. Then factor it out of the expression. Write as prime factors. Circle common primes Find the GMF (multiply the common primes). Use the distributive property to factor out the GMF Check – Multiply the factors together using the distributive property. Whatever is NOT circled goes in parentheses.

Find the greatest monomial factor. Then factor it out of the expression. The problem. Think of the GMF. Use the distributive property to factor out the GMF

Find the greatest monomial factor. Then factor it out of the expression. Write as prime factors. Circle common primes prime

Find the greatest monomial factor. Then factor it out of the expression. Check – Multiply the factors together using the distributive property. Example 1 Example 2

Example 1 Find the greatest monomial factor. Then factor it out of the expression. Check – Multiply the factors together using the distributive property. ( )

Example 2 Find the greatest monomial factor. Then factor it out of the expression. Check – Multiply the factors together using the distributive property. ( )

Example 3 Find the greatest monomial factor. Then factor it out of the expression. Example 4 Example 5 Example 6

Using the distributive property to factor polynomials having four or more terms is called factoring by grouping because pairs of terms are grouped together and factored. The distributive property is then applied a second time to factor a common binomial factor. Group terms with common factors. Factor the GMF from each group. Factor the common binomial factor. Check – Multiply the factors together using FOIL. The problem.

Sometimes you can group terms in more than one way when factoring a polynomial. Here is an alternate way to group the previous problem. Group terms with common factors. Factor the GMF from each group. Factor the common binomial factor. Notice that this result is as the previous grouping. The problem.

Factor the polynomial. Check – Multiply the factors together using FOIL. Example 7 Example 8 Example 9 Example 10

Factor the polynomial. Check – Multiply the factors together using FOIL. Example 7 Example 8 Undo double sign!

Factor the polynomial. Check – Multiply the factors together using FOIL. Example 9 Example 10

8-A3 Page 423 # 19–27, and Page 429 # 9–20.