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8-4A Factoring Trinomials when the Leading Coefficient isn’t 1. X-Factor method Algebra 1 Glencoe McGraw-HillLinda Stamper.

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Presentation on theme: "8-4A Factoring Trinomials when the Leading Coefficient isn’t 1. X-Factor method Algebra 1 Glencoe McGraw-HillLinda Stamper."— Presentation transcript:

1 8-4A Factoring Trinomials when the Leading Coefficient isn’t 1. X-Factor method Algebra 1 Glencoe McGraw-HillLinda Stamper

2 x + 2 Factoring quadratic trinomials means finding the binomial factors when given a product. The factors represent the length and width of the rectangle. You are given the product – quadratic trinomial! You need to find the factors!

3 Check by doing FOIL in your head! All of the previous problems involving quadratic trinomials had a leading coefficient of 1. Multiply a times c to find the product. b in the bottom represents the sum –3 –2 –3 1 You know there will be an x in each factor!

4 Today’s problems involve factoring quadratic trinomials when the leading coefficient isn’t 1 - this includes negative 1. To factor quadratic trinomials when the leading coefficient isn’t 1, you will use the X figure and then factor out the greatest monomial factor (aka greatest common factor).

5 + 2 Step 1 Use the X figure as you did when the leading coefficient was 1. Multiply a times c to find the product. b in the bottom represents the sum –10 –3 –5 2 ( )( ) Step 2 Take the coefficient “a” and the x from the ax 2 term and the numbers from the sides of your X figure and place them into two parentheses in the following manner. – 5 Step 3 Factor out the greatest monomial factor from each parentheses if you can. Step 4 Discard the factor/s you pull out after X figure. Step 5 Check using FOIL.

6 + 2 –10 –3 –5 2 ( )( ) – 5 Check using FOIL. after You must discard (X out) the GMF that is pulled out after using the X figure!

7 Before you use the X figure, you must factor out any greatest monomial factor, if possible! DO NOT DISCARD THIS FACTOR! before You must keep the GMF that is pulled out before using the X figure!

8 ( )( ) Factor Check using FOIL. If you factor out a GMF: before using the X figure, keep it, after using the X figure, discard it.

9 before Factor out a GMF before the X figure – you must keep it! after Factor out a GMF after the X figure – discard it (X it out)!

10 –4 5 A polynomial that cannot be written as a product of two polynomials with integral coefficients is called a prime polynomial! Try this problems...

11 Example 1 Factor. Example 2 Example 3 Example 4 Example 5 Copy all of the above problems before you start to factor! Example 6 Example 7

12 ( )( ) Example 1 Factor Check using FOIL. Can you factor out a greatest monomial factor?

13 ( )( ) Example Check using FOIL. Can you factor out a greatest monomial factor? Factor ( )( ) Example Can you factor out a greatest monomial factor? If you factor out a GMF: before using the X figure, keep it, after using the X figure, discard it.

14 Example 4 Can you factor out a greatest monomial factor? Factor ( )( ) Example Check using FOIL. Can you factor out a greatest monomial factor?

15 2 -6 ( )( ) Example Check using FOIL. Can you factor out a greatest monomial factor? Factor (10x - 8)(10x - 35) Example Check using FOIL. Can you factor out a greatest monomial factor? Make an organized list of factors

16 Example 1 Factor. Example 2 Example 3 Example 4 Example 5 Example 6 Example 7

17 8-A9 Page # 11–22,44,46-51.


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