Algebra 1 Practice Test: Factoring Quadratic Trinomials
- Factoring Quadratic Trinomials
- 10 questions
- 13 minutes
These 10 questions practice factoring quadratics with a = 1 and a ≠ 1, special patterns and the greatest common factor. Check each answer by multiplying the factors back out.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
Factor x2 + 7x + 12.
Correct answer: D
Find two numbers that multiply to 12 and add to 7: 3 and 4. The pair 2 and 6 also multiplies to 12 but adds to 8.
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Question 2
Factor x2 − 2x − 15.
Correct answer: B
The numbers must multiply to −15 and add to −2: −5 and 3. (x + 5)(x − 3) gives a middle term of +2x.
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Question 3
Factor x2 − 49.
Correct answer: C
This is a difference of squares: a2 − b2 = (a − b)(a + b) with b = 7. (x − 7)2 would produce a middle term of −14x.
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Question 4
Factor out the greatest common factor: 6x3 − 9x2.
Correct answer: A
The GCF of 6 and 9 is 3, and the GCF of x3 and x2 is x2. Dividing each term by 3x2 leaves 2x − 3.
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Question 5
Factor 2x2 + 7x + 3.
Correct answer: D
Check the middle term: (2x + 1)(x + 3) gives 6x + x = 7x. (2x + 3)(x + 1) gives only 5x.
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Question 6
Factor 3x2 − 10x − 8.
Correct answer: B
Multiplying out gives 3x2 − 12x + 2x − 8 = 3x2 − 10x − 8. (3x − 2)(x + 4) gives +10x, the wrong sign.
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Question 7
Factor x2 − 10x + 25.
Correct answer: A
This is a perfect square trinomial: −5 times −5 is 25 and −5 plus −5 is −10. (x − 5)(x + 5) would give x2 − 25.
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Question 8
Factor completely: 2x2 − 18.
Correct answer: C
First take out the GCF 2: 2(x2 − 9). Then factor the difference of squares: 2(x − 3)(x + 3).
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Question 9
Which binomial is a factor of x2 + x − 20?
Correct answer: B
The trinomial factors as (x + 5)(x − 4) because 5 · (−4) = −20 and 5 + (−4) = 1. So x + 5 is a factor, but x + 4 is not.
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Question 10
Solve x2 − 5x − 14 = 0 by factoring.
Correct answer: A
Factor: (x − 7)(x + 2) = 0, so x − 7 = 0 or x + 2 = 0. Taking the numbers in the factors without changing sign gives −7 and 2.
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