This topic focuses on practicing how to factorize quadratic equations by finding common factors among the terms. Specifically, students are prompted to identify common factors within the first two terms and the last two terms of each equation, split the terms accordingly, and then solve to find the factors that multiply to form the quadratic expression. Each problem presents a quadratic expression, and students must choose the correct factorization from multiple choices. This is a critical skill within the broader unit of factoring polynomials, particularly those with leading coefficients.

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

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Factor the Quadratic Equation with Coefficient - Split X Terms To Answer Worksheet

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Factor the Quadratic Equation with Coefficient - Split X Terms To Ans...
1
Find common factors of the first 2 and last 2 terms, and solve.
A LaTex expression showing 49p to the power of 2 + 35p + 21p + 15
a A LaTex expression showing (p + 5)(56p + 3)
b A LaTex expression showing (56p + 5)(7p + 3)
c A LaTex expression showing (7p + 5)(7p + 3)
d A LaTex expression showing (7p + 5)(p + 3)
e A LaTex expression showing (15p + 5)(p - 3)
2
Find common factors of the first 2 and last 2 terms, and solve.
A LaTex expression showing 6t to the power of 2 + 8t - 9t - 12
a A LaTex expression showing (3t - 4)(t + 3)
b A LaTex expression showing (2t - 4)(23t - 3)
c A LaTex expression showing (3t + 4)(2t - 3)
d A LaTex expression showing (1t - 4)(3t + 3)
e A LaTex expression showing (12t + 4)(t - 3)
3
Find common factors of the first 2 and last 2 terms, and solve.
A LaTex expression showing 56x to the power of 2 + 49x + 48x + 42
a A LaTex expression showing (97x - 7)(8x + 6)
b A LaTex expression showing (42x + 7)(x - 6)
c A LaTex expression showing (7x - 7)(42x + 6)
d A LaTex expression showing (7x + 7)(42x + 6)
e A LaTex expression showing (8x + 7)(7x + 6)
4
Find common factors of the first 2 and last 2 terms, and solve.
A LaTex expression showing 14m to the power of 2 + 35m + 12m + 30
a A LaTex expression showing (47m + 5)(2m + 6)
b A LaTex expression showing (7m + 5)(72m - 6)
c A LaTex expression showing (7m + 5)(m + 6)
d A LaTex expression showing (2m + 5)(7m + 6)
e A LaTex expression showing (30m + 5)(m - 6)
5
Find common factors of the first 2 and last 2 terms, and solve.
A LaTex expression showing 25m to the power of 2 + 40m - 20m - 32
a A LaTex expression showing (5m + 8)(m + 4)
b A LaTex expression showing (20m - 8)(5m + 4)
c A LaTex expression showing (5m + 8)(5m - 4)
d A LaTex expression showing (20m + 8)(5m - 4)
e A LaTex expression showing (5m - 8)(55m - 4)
6
Find common factors of the first 2 and last 2 terms, and solve.
A LaTex expression showing 27m to the power of 2 + 63m + 12m + 28
a A LaTex expression showing (9m + 7)(m + 4)
b A LaTex expression showing (75m - 7)(3m + 4)
c A LaTex expression showing (3m + 7)(9m + 4)
d A LaTex expression showing (75m + 7)(3m + 4)
e A LaTex expression showing (m - 7)(75m + 4)
7
Find common factors of the first 2 and last 2 terms, and solve.
A LaTex expression showing 45y to the power of 2 + 25y - 18y - 10
a A LaTex expression showing (9y + 5)(5y - 2)
b A LaTex expression showing (5y - 5)(10y + 2)
c A LaTex expression showing (5y - 5)(59y - 2)
d A LaTex expression showing (y + 5)(7y - 2)
e A LaTex expression showing (7y - 5)(9y + 2)
8
Find common factors of the first 2 and last 2 terms, and solve.
A LaTex expression showing 14r to the power of 2 + 6r + 49r + 21
a A LaTex expression showing (55r + 3)(7r + 7)
b A LaTex expression showing (r + 3)(55r + 7)
c A LaTex expression showing (r - 3)(55r + 7)
d A LaTex expression showing (7r + 3)(2r + 7)
e A LaTex expression showing (55r - 3)(7r + 7)