Factor Trinomials Using the AC Method

Unit 9 - Test Review

By John Campbell

Part 1 - Factoring

​Can you factor in all these methods for the following cases?

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CHECK FOR GCF FIRST!

Before using any of the methods be sure to check for a GCF, and factor it out.

Subject | Subject

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• 4 terms.​

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​Factoring by Grouping.

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Multiple Choice

Factor completely

•   $$\left(1+3m\right)\left(m^2-8\right)$$  

• $$-1\left(m^2+8\right)\left(-3m+1\right)$$   

• $$\left(9n-1\right)\left(n-3\right)\left(n+3\right)$$  

•   $$\left(-m^2-8\right)\left(-3m+1\right)$$  

Multiple Choice

Factor completely.

• $$\left(9n-1\right)\left(n^2-9\right)$$  

• $$\left(9n-1\right)\left(n-3\right)^2$$  

• $$\left(9n-1\right)\left(n-3\right)\left(n+3\right)$$  

• $$9\left(n-9\right)\left(n+1\right)$$  

• Factoring by grouping is a step.

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The ac-method​

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Multiple Choice

• (3p-5)(p-1)

• (3p+1)(p+5)

• (3p-1)(p+5)

• (3p-1)(p-5)

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• First and last terms are perfect squares.

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Special Cases​

Multiple Choice

• $$\left(3n-2\right)^2$$  

• $$\left(3n-2\right)\left(3n+2\right)$$  

• $$\left(3n+2\right)^2$$  

• $$3\left(3n-1\right)^2$$  

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a=1

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• Two factors of c that sum to b.

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Multiple Choice

• 2(x+13)(x+14)

• 2(x+13)(x+1)

• (2x-14)(x+2)

• 2(x+7)(x+2)

Draw

Factor completely.

Draw

Factor completely.

Part 2 - Multiplying.

​Can you multiply with these techniques? Do you know when to use each one?

Case 1)  Monomial into Polynomial

• Distribution

Case 2) Binomial by binomial  ​

• FOIL

• Special Patterns

Case 2) Polynomial by polynomial

• Distribute each term of the 1st polynomial into each term of the next polynomial.  ​

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Draw

Multiply.

Draw

Multiply.

Part 3 - Adding and Classifying.

​Can you correctly identify and combine like terms?

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Can you identify a polynomial by it's degree and number of terms?​

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Draw

Subtract. Write your answer in Standard Form.

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