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**8-4A Factoring Trinomials when the Leading Coefficient isn’t 1.**

X-Factor method Algebra Glencoe McGraw-Hill Linda Stamper

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

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**Multiply a times c to find the product. –3**

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

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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).

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**Step 1 Use the X figure as you did when the leading coefficient was 1.**

–10 Multiply a times c to find the product. – 5 –5 + 2 2 –3 b in the bottom represents the sum Step 2 Take the coefficient “a” and the x from the ax2 term and the numbers from the sides of your X figure and place them into two parentheses in the following manner. ( )( ) 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.

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**–3 –10 2 – 5 –5 + 2 ( )( ) Check using FOIL.**

You must discard (X out) the GMF that is pulled out after using the X figure! ( )( ) Check using FOIL.

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**DO NOT DISCARD THIS FACTOR!**

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

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Factor. -10 - 5 -5 + 2 2 -3 ( )( ) If you factor out a GMF: before using the X figure, keep it, after using the X figure, discard it. Check using FOIL.

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**Factor out a GMF before the X figure – you must keep it! **

Factor out a GMF after the X figure – discard it (X it out)!

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

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**Copy all of the above problems before you start to factor!**

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

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**Can you factor out a greatest monomial factor?**

Example 1 Factor. 6 + 3 3 + 2 2 5 Can you factor out a greatest monomial factor? ( )( ) Check using FOIL.

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**before using the X figure, keep it, **

Factor. Example 2 Example 3 -22 -18 + 22 22 - 1 -1 Can you factor out a greatest monomial factor? Can you factor out a greatest monomial factor? + 6 6 - 3 -3 21 3 ( )( ) ( )( ) Check using FOIL. If you factor out a GMF: before using the X figure, keep it, after using the X figure, discard it.

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**Factor. Example 4 Example 5 36 + 9 9 + 4 4 13 ( )( ) Check using FOIL.**

Can you factor out a greatest monomial factor? Can you factor out a greatest monomial factor? 13 ( )( ) Check using FOIL.

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**Factor. Example 6 Example 7 280 -12 - 6 -6 + 2 2 -8 -35 -4 -43**

Make an organized list of factors. 1•280 2•140 4 •70 5 •56 7 •40 8 •35 280 -12 - 6 -6 + 2 2 -8 -35 Can you factor out a greatest monomial factor? Can you factor out a greatest monomial factor? -4 -43 (10x - 8)(10x - 35) ( )( ) Check using FOIL. Check using FOIL.

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

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Homework 8-A9 Page # 11–22,44,46-51.

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