Factoring Polynomials: Algebra 1 Math Test – PDF Download

Question 1: Greatest common factor (2 points)

Factor out the greatest common factor.

1. \(15 x^{3} – 10 x^{2}\) (1 point)
2. \(12 a^{2} b + 18 a b^{2}\) (1 point)

Question 2: Factor trinomials (2 points)

Factor each trinomial.

1. \(x^{2} + 11 x + 24\) (1 point)
2. \(x^{2} – 4 x – 21\) (1 point)

Question 3: Factor with a leading coefficient (2 points)

Factor each trinomial.

1. \(3 x^{2} + 10 x + 8\) (1 point)
2. \(4 x^{2} – 8 x – 5\) (1 point)

Question 4: Special patterns (2 points)

Factor.

1. \(49 x^{2} – 36\) (1 point)
2. \(9 x^{2} + 30 x + 25\) (1 point)

Question 5: Factor by grouping (2 points)

Factor each polynomial by grouping.

1. \(x^{3} + 5 x^{2} + 2 x + 10\) (1 point)
2. \(3 x^{3} – 6 x^{2} – 4 x + 8\) (1 point)

Question 6: Factor completely (3 points)

Factor completely.

1. \(3 x^{2} – 48\) (1 point)
2. \(2 x^{3} + 12 x^{2} + 18 x\) (1 point)
3. \(6 x^{2} – 5 x – 4\) (1 point)

Question 7: Zeros and the graph (3 points)

The graph of \(y=x^{2}-x-6\) is shown.

1. Factor \(x^{2}-x-6\). (1 point)
2. Solve \(x^{2}-x-6=0\). (1 point)
3. Label the x-intercepts on the graph by writing their coordinates. (1 point)

Question 8: Poster dimensions (2 points)

A rectangular poster has area \(2x^{2}+11x+12\) square inches and width \(x+4\) inches.

1. Write an expression for the length. (1 point)
2. Find the length and width when \(x=5\). (1 point)

Question 9: Is it complete? (2 points)

Aisha factors \(4x^{2}-100\) as \((2x-10)(2x+10)\).

1. Explain why the factorization is not complete. (1 point)
2. Write the complete factorization. (1 point)

⬇ Download the Algebra 1 Factoring Polynomials test (PDF, 90 KB)

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