Polynomials Test Answer Key with Scoring – Algebra 1

Question 1 Standard Form (2 points)

Standard form: −2x³ + 9x² + 5x − 4. Degree 3, leading coefficient −2.

Scoring: 1 point for the correct order, 1 point for degree and leading coefficient.

Question 2 Add Polynomials (2 points)

6 − 2 = 4, −4 + 9 = 5, 7 − 3 = 4.

4x² + 5x + 4

Scoring: 1 point for the x² term, 1 point for the other two terms.

Question 3 Subtract Polynomials (2 points)

8x² + 3x − 5 − 5x² + 6x − 2 = 3x² + 9x − 7.

3x² + 9x − 7

Scoring: 1 point for distributing the minus sign, 1 point for the result.

Question 4 Area of a Rectangle (2 points)

(7x + 2)(4x − 5) = 28x² − 35x + 8x − 10 = 28x² − 27x − 10.

28x² − 27x − 10

Scoring: 1 point for the four products, 1 point for combining like terms.

Question 5 Trinomial Times Binomial (3 points)

x · (x² + 5x − 2) = x³ + 5x² − 2x. −3 · (x² + 5x − 2) = −3x² − 15x + 6.

Combine: x³ + 2x² − 17x + 6.

x³ + 2x² − 17x + 6

Scoring: 1 point for each row of products, 1 point for the final combination.

Question 6 Special Products (2 points)

1. 16x² − 24x + 9.
2. 4x² − 49.

Scoring: 1 point per part.

Question 7 Grass Around the Pool (3 points)

1. (2x + 7)(x + 4) − (x + 1)² = 2x² + 15x + 28 − (x² + 2x + 1) = x² + 13x + 27.
2. 25 + 65 + 27 = 117 square feet. Check: yard 17 × 9 = 153, pool 6² = 36, and 153 − 36 = 117.

Scoring: (a) 1 point for the two areas, 1 point for the simplified result. (b) 1 point.

Question 8 Mental Math with Algebra (2 points)

1. (40 − 2)(40 + 2) = 1600 − 4 = 1,596.
2. (70 + 1)² = 4900 + 140 + 1 = 5,041.

Scoring: 1 point per part for a correct structure and value.

Question 9 Explain the Error (2 points)

Dev squared each term but skipped the cross products. (x + 5)² means (x + 5)(x + 5) = x² + 5x + 5x + 25.

Correct: x² + 10x + 25

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