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Factoring Polynomials: GCF and Grouping

Factoring Polynomials: GCF and Grouping. Mod. 4, Topic 1, Sec. 4. Objectives. I can factor polynomials by GCF. I can factor polynomials by grouping. I can apply factoring polynomials to real world scenarios. Opening.

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Factoring Polynomials: GCF and Grouping

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  1. Factoring Polynomials: GCF and Grouping Mod. 4, Topic 1, Sec. 4

  2. Objectives • I can factor polynomials by GCF. • I can factor polynomials by grouping. • I can apply factoring polynomials to real world scenarios.

  3. Opening • Think back to number sense that you learned back in elementary school. What does it mean to find the GCF? • What is the GCF of 30 & 125? • What is the GCF of and ? • Today, we are going to use the GCF to factor out polynomial expressions. GCF = 5 GCF =

  4. Divisibility Rules • Divisibility – a number can go evenly into another number. • The following divisibility rules will help you significantly when dealing with factors. • 2: the number ends in an even number. • 3: the sum of the digits is divisible by 3. • 5: the number ends in a 0 or 5. • 6: the number is divisible by 2 & 3. • 9: the sum of the digits is divisible by 9. • 10 : the number ends in 0.

  5. Factoring Polynomials

  6. Factoring Polynomials • To factor an expression means to rewrite the expression as a product of factors. • There are many different methods of factoring. • Today, we are going to look at simply using the GCF to factor our expressions.

  7. Method 1: Factoring by GCF • To factor by GCF, you must have a polynomial that has a common factor amongst its terms. • Steps to GCF factoring: • Find the GCF of the terms of the polynomial (coefficients AND variables). • Simplify the expression by dividing the coefficients by the GCF and subtracting the GCF variable. • Write answer as GCF(simplified expressions)

  8. Factoring by GCF Example (pg. M4-60) What happens if we change the expression to ?

  9. Practice Problems: pg. M4-60 Problem 1

  10. Try it out! - Factor each expression using the GCF.

  11. Taking it up a notch. What about if I asked you to factor this expression? What do you notice?

  12. Method 2: Factoring by Grouping • GCF factoring will not work in all cases, so we have to try something else. • Another option would be to Factor by Grouping. • Steps to Factor by Grouping: • Group the terms in pairs. • Find the GCF of each pair and factor as normal. • If the remaining simplified expressions are the same, REFACTOR the expressions as (Common Simplified Expressions) (GCF’s).

  13. Factoring by Grouping

  14. Try it out! - Factor each expression.

  15. Try it out, Part 2! – Factor each expression.

  16. Applying Factoring to Real World Problems

  17. Applying Factoring Steven is building a rectangular garden with an area of . • What would two possible dimensions of his garden have to be to fit this area? • What would the perimeter of this garden be? 2x(-4x+6) -4x + 12

  18. Closing

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