Factoring Polynomials: Algebra 1 Math Quiz – PDF Download
Answer these 10 multiple-choice questions on factoring: GCF, trinomials, the special patterns, grouping and zeros of quadratics. Each has one correct answer, and each explanation points out a typical mistake.
Algebra 1Common Core: A-SSE.A.2 · A-SSE.B.3a
🎯 Factoring Polynomials – Algebra 1 math quiz
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Question 1
What is the greatest common factor of \(24x^{3}\) and \(36x^{2}\)?
A\(6x^{2}\)
B\(12x^{2}\)
C\(12x^{3}\)
D\(72x^{3}\)
Question 2
Factor \(6x^{2}-9x\) completely.
A\(3(2x^{2}-3x)\)
B\(3x(2x+3)\)
C\(3x(2x-3)\)
D\(x(6x-9)\)
Question 3
Factor \(x^{2}+9x+20\).Area model.
A\((x+4)(x+5)\)
B\((x+2)(x+10)\)
C\((x+4)(x-5)\)
D\((x-4)(x-5)\)
Question 4
Factor \(x^{2}-2x-24\).
A\((x+6)(x-4)\)
B\((x-6)(x+4)\)
C\((x-8)(x+3)\)
D\((x-6)(x-4)\)
Question 5
Factor \(25x^{2}-49\).
A\((5x-7)^{2}\)
B\((5x+7)^{2}\)
C\((25x-7)(x+7)\)
D\((5x-7)(5x+7)\)
Question 6
Factor \(4x^{2}+12x+9\).
A\((4x+3)^{2}\)
B\((2x+3)(2x-3)\)
C\((2x+3)^{2}\)
D\((4x+3)(x+3)\)
Question 7
Factor \(2x^{2}+5x-3\).
A\((2x+1)(x-3)\)
B\((2x-3)(x+1)\)
C\((2x+3)(x-1)\)
D\((2x-1)(x+3)\)
Question 8
The graph shows \(y=x^{2}-x-12\). What are the solutions of \(x^{2}-x-12=0\)?Graph of the parabola.
A\(x=4\) and \(x=3\)
B\(x=4\) and \(x=-3\)
C\(x=-4\) and \(x=3\)
D\(x=12\) and \(x=-1\)
Question 9
Factor \(x^{3}+3x^{2}+4x+12\) by grouping.
A\((x^{2}+4)(x+3)\)
B\((x^{2}+3)(x+4)\)
C\((x^{2}+4)(x-3)\)
D\((x^{2}-4)(x+3)\)
Question 10
A rectangle has area \(x^{2}+8x+12\) and width \(x+2\). What is its length?Rectangle.
A\(x+4\)
B\(x+10\)
C\(x+6\)
D\(x+14\)
🎉 Quiz complete!
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Remember:
Always factor out the greatest common factor first.
For x² + bx + c, find two numbers with product c and sum b.
For ax² + bx + c, split the middle term using two numbers with product ac, then factor by grouping.
Patterns: a² − b² = (a + b)(a − b) and a² ± 2ab + b² = (a ± b)².
The zero product property turns a factored equation into its zeros, the x-intercepts of the graph.
