Factoring Polynomials Test Answer Key with Scoring – Algebra 1

Question 1 Greatest Common Factor (2 points)

GCF: 5x²y. Dividing gives 4x and 7y.

5x²y(4x − 7y)

Scoring: 1 point for the correct GCF, 1 point for the second factor.

Question 2 Two Trinomials (2 points)

1. Product 36, sum −13: −4 and −9. (x − 4)(x − 9)
2. Product −45, sum 4: 9 and −5. (x + 9)(x − 5)

Scoring: 1 point per part.

Question 3 Difference of Squares (2 points)

1. (9x + 4)(9x − 4)
2. (5 + 7y)(5 − 7y)

Scoring: 1 point per part.

Question 4 Perfect Squares (2 points)

1. (2x)², 7² and 2(2x)(7) = 28x: (2x + 7)²
2. x², 9² and −2(x)(9) = −18x: (x − 9)²

Scoring: 1 point per part.

Question 5 Leading Coefficient Not 1 (3 points)

ac = −60 and the sum is −11: −15 and 4. Split: 6x² − 15x + 4x − 10 = 3x(2x − 5) + 2(2x − 5).

(3x + 2)(2x − 5)

Scoring: 1 point for the correct pair of numbers, 1 point for grouping, 1 point for the final factors.

Question 6 Factor by Grouping (2 points)

4x²(x + 3) − 5(x + 3).

(4x² − 5)(x + 3)

Scoring: 1 point for grouping correctly, 1 point for the final factors.

Question 7 Zeros from a Graph (3 points)

1. Product −35, sum −2: −7 and 5. f(x) = (x − 7)(x + 5)
2. Set each factor to 0: x = 7 and x = −5.
3. They are the x-intercepts: the graph crosses the x-axis at (−5, 0) and (7, 0).

Scoring: 1 point per part.

Question 8 Garden Dimensions (2 points)

Factor: 2x² + 13x + 15 = (2x + 3)(x + 5).

Length 2x + 3 feet

Scoring: 1 point for factoring the area, 1 point for identifying the length.

Question 9 Factor Completely (2 points)

5x² − 45 = 5(x² − 9) = 5(x + 3)(x − 3).

5(x + 3)(x − 3). Each binomial is linear, so none can be factored further.

Scoring: 1 point for the factorization, 1 point for the explanation.