Homework Help Ch 8-4.

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Presentation transcript:

Homework Help Ch 8-4

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!

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.

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 monomial factor/s you pulled out. Step 5 Check using FOIL.

–3 –10 2 – 5 –5 + 2 ( )( ) Check using FOIL. You must throw away the greatest monomial factor that is pulled out after using the X figure! ( )( ) Check using FOIL.

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 greatest monomial factor that is pulled out before using the X figure! DO NOT DISCARD THIS FACTOR!

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.

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

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.

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.

Factor. Example 4 Example 5 36 -12 + 9 9 + 4 4 - 6 -6 + 2 2 13 -4 Can you factor out a greatest monomial factor? Can you factor out a greatest monomial factor? 13 -4 ( )( ) ( )( ) Check using FOIL. Check using FOIL.

Homework 445 # 11 – 30 Graph: .