Factor the Quadratic Equation with Coefficient (Level 2)

This math topic focuses on advanced algebraic skills involving the factorization of quadratic equations with coefficients. It is part of a broader unit on polynomials and quadratics. Students are given quadratic expressions and must select the equivalent factored expression from multiple choices. Each question presents a quadratic equation with a latex-rendered image, and students need to choose the correct factorization, also provided as latex-rendered images. This exercise helps develop proficiency in recognizing different forms of quadratic expressions and transforms them into product forms involving binomials.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Algebraic Functions - Factor the Quadratic Equation with Coefficient Worksheet

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Algebraic Functions - Factor the Quadratic Equation with Coefficient
1
Which answer is the same expression as this
A LaTex expression showing 12c to the power of 2 + 60c + 72
a A LaTex expression showing (3c + 8)(c + 9)
b A LaTex expression showing (4c + 8)(3c + 9)
c A LaTex expression showing (4c + 8)(c + 9)
d A LaTex expression showing (60c - 8)(4c + 9)
e A LaTex expression showing (72c - 8)(c + 9)
f A LaTex expression showing (3c + 8)(34c - 9)
2
Which answer is the same expression as this
A LaTex expression showing 24z to the power of 2 - 0z - 24
a A LaTex expression showing (0z - 4)(4z + 6)
b A LaTex expression showing (4z - 4)(z + 6)
c A LaTex expression showing (6z + 4)(z + 6)
d A LaTex expression showing (4z + 4)(6z - 6)
e A LaTex expression showing (24z - 4)(z + 6)
f A LaTex expression showing (6z - 4)(64z - 6)
3
Which answer is the same expression as this
A LaTex expression showing 12m to the power of 2 + 6m - 18
a A LaTex expression showing (6m - 9)(6m + 2)
b A LaTex expression showing (2m + 9)(m + 2)
c A LaTex expression showing (2m - 9)(26m - 2)
d A LaTex expression showing (18m - 9)(m + 2)
e A LaTex expression showing (6m + 9)(2m - 2)
f A LaTex expression showing (6m - 9)(m + 2)
4
Which answer is the same expression as this
A LaTex expression showing 18m to the power of 2 + 42m + 12
a A LaTex expression showing (42m - 6)(3m + 2)
b A LaTex expression showing (6m + 6)(m + 2)
c A LaTex expression showing (3m + 6)(m + 2)
d A LaTex expression showing (3m + 6)(6m + 2)
e A LaTex expression showing (12m - 6)(m + 2)
f A LaTex expression showing (6m + 6)(63m - 2)
5
Which answer is the same expression as this
A LaTex expression showing 24x to the power of 2 - 6x - 18
a A LaTex expression showing (6x - 6)(8x + 3)
b A LaTex expression showing (8x + 6)(3x - 3)
c A LaTex expression showing (3x - 6)(38x - 3)
d A LaTex expression showing (3x + 6)(x + 3)
e A LaTex expression showing (18x - 6)(x + 3)
f A LaTex expression showing (8x - 6)(x + 3)
6
Which answer is the same expression as this
A LaTex expression showing 24m to the power of 2 + 26m - 63
a A LaTex expression showing (4m + 9)(6m - 7)
b A LaTex expression showing (6m - 9)(64m - 7)
c A LaTex expression showing (4m - 9)(m + 7)
d A LaTex expression showing (63m - 9)(m + 7)
e A LaTex expression showing (6m + 9)(m + 7)
f A LaTex expression showing (26m - 9)(4m + 7)
7
Which answer is the same expression as this
A LaTex expression showing 72n to the power of 2 + 91n + 24
a A LaTex expression showing (8n + 3)(n + 8)
b A LaTex expression showing (9n + 3)(n + 8)
c A LaTex expression showing (91n - 3)(8n + 8)
d A LaTex expression showing (9n + 3)(98n - 8)
e A LaTex expression showing (24n - 3)(n + 8)
f A LaTex expression showing (8n + 3)(9n + 8)
8
Which answer is the same expression as this
A LaTex expression showing 40b to the power of 2 + 33b - 18
a A LaTex expression showing (5b - 6)(b + 3)
b A LaTex expression showing (18b - 6)(b + 3)
c A LaTex expression showing (5b + 6)(8b - 3)
d A LaTex expression showing (8b - 6)(85b - 3)
e A LaTex expression showing (33b - 6)(5b + 3)
f A LaTex expression showing (8b + 6)(b + 3)