AC Method Factoring Worksheet
Grade 12 Math worksheet focusing on factoring quadratic trinomials using the AC Method.
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AC Method Factoring Worksheet
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Read each question carefully and factor the given quadratic expressions using the AC Method. Show all your work.
1. In a quadratic expression of the form ax² + bx + c, the first step of the AC method is to multiply 'a' and 'c' to get the product.
2. Next, find two numbers that multiply to the AC product and add to the term, 'b'.
3. Rewrite the middle term (bx) as the sum or difference of two terms using the two numbers found in the previous step. This process is called the middle term.
4. After splitting the middle term, factor the resulting four-term polynomial by .
Factor the following quadratic trinomials using the AC Method.
5. 2x² + 7x + 3
6. 3x² - 10x + 8
7. 6x² + x - 12
8. 4x² - 16x + 15
9. Which of the following is a factor of 5x² + 13x - 6?
(5x - 2)
(x - 3)
(5x + 3)
(x + 2)
10. When factoring 12x² - 17x + 6 using the AC method, what two numbers should be used to split the middle term?
-9 and -8
9 and 8
-12 and -5
12 and 5
11. The AC method can only be used when the 'a' coefficient is 1.
True
False
12. Factoring by grouping is a critical step in the AC method after splitting the middle term.
True
False
Factor the following quadratic trinomials completely. Remember to look for a Greatest Common Factor (GCF) first.
13. 18x² + 33x + 9
14. -4x² + 2x + 30