Chapter 5 Section 4 Factoring Quadratic Expressions.

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Presentation transcript:

Chapter 5 Section 4 Factoring Quadratic Expressions

Factoring – rewriting an expression as the product of its factors Greatest Common Factor of an expression – GCF is the common factor with the greatest coefficient and the greatest exponent The largest number and variable that will go into everything Binomial – an expression with two terms ex: 2x+3 Trinomial – an expression with three terms ex: x 2 + 5x -94

Factor each expression. What is the largest number common to all terms? Write it on the outside of the parenthesis What is the greatest exponent on the variables that is common to all? Write it beside the first number. In parenthesis write what is left when you divide the term by the expression written.

Try These Problems.

Public Service Announcement There are many ways to factor. You learned in Alg I how to factor. Pay attention, if the method taught then did not click, hopefully one of today’s methods will. I will not specify how you have to factor, as long as you are doing it correctly. Factoring DOES NOT GO AWAY, we use it all year and for the rest of math. Be sure you understand how or seek out help now!!!

“Formal Factoring” AKA: factor and sum method note this will always work ax 2 + bx + c 1. Find factors of a∙c (the first times the last) 2. Find the sum of the factors 3. Choose the factors whose sum is b 4. Rewrite the linear term using the factors you found 5. Take the GCF out of the first two terms, then the second leaving two identical binomials 6. Rewrite using the identical binomial and what is on the outside as the other binomial Check: (FOIL) Multiply the binomials

3x x + 5 Factors of Sum of Factors Step 1: Step 2: Step 4: Step 5: Step 6: Check:

X 2 + 8x + 7 Factors of Sum of Factors

X x + 72 Factors of Sum of Factors

X 2 - x - 12 Factors of Sum of Factors

“Informal Factoring” ax 2 + bx + c What numbers multiply to give me a? c? What signs should I use? Do the combinations add to give me b?

This one has a catch so watch carefully

Factoring Day 2: Special Expressions There are some expressions that can be factored by following patterns

Perfect Square Trinomial The product when you square a binomial (a + b) 2 = a 2 + 2ab + b 2 (a - b) 2 = a 2 - 2ab + b 2 This pattern can be used to factor: 9x 2 – 42x x x + 9

Difference of Two Squares (a - b)(a + b) = a 2 - b 2 This pattern can be used to factor: x 2 – 64 4a