This math topic focuses on factoring quadratic expressions that include a leading coefficient. Specifically, it helps develop the skill to identify and consolidate shared bracketed factors within quadratic expressions to simplify them into a product of binomials. Each problem presents a quadratic expression with a common binomial factor in its terms, and the task is to factor out this common element correctly. The problems increase in complexity, supporting the learning of polynomials factoring in quadratics involving distinct arithmetic strategies and algebraic manipulation.

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 - Partial Answer to Answer Worksheet

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Factor the Quadratic Equation with Coefficient - Partial Answer to An...
1
Consolidate the shared, bracketed factors to simplify
A LaTex expression showing 5p(p + 4) + 8(p + 4)
a A LaTex expression showing (p + 4)(5p + 8)
b A LaTex expression showing (5p + 4)(52p - 8)
2
Consolidate the shared, bracketed factors to simplify
A LaTex expression showing 7t(2t + 3) + 8(2t + 3)
a A LaTex expression showing (37t + 3)(2t + 8)
b A LaTex expression showing (2t + 3)(7t + 8)
3
Consolidate the shared, bracketed factors to simplify
A LaTex expression showing 9m(4m + 9) + 4(4m + 9)
a A LaTex expression showing (36m - 9)(m + 4)
b A LaTex expression showing (4m + 9)(9m + 4)
4
Consolidate the shared, bracketed factors to simplify
A LaTex expression showing 9r(7r + 6) + 7(7r + 6)
a A LaTex expression showing (7r + 6)(9r + 7)
b A LaTex expression showing (r - 6)(103r + 7)
5
Consolidate the shared, bracketed factors to simplify
A LaTex expression showing 4m(m + 9) + 5(m + 9)
a A LaTex expression showing (m + 9)(4m + 5)
b A LaTex expression showing (4m + 9)(m + 5)
6
Consolidate the shared, bracketed factors to simplify
A LaTex expression showing 6q(6q + 7) + 5(6q + 7)
a A LaTex expression showing (6q + 7)(6q + 5)
b A LaTex expression showing (q - 7)(72q + 5)
7
Consolidate the shared, bracketed factors to simplify
A LaTex expression showing 8m(m + 4) + 7(m + 4)
a A LaTex expression showing (m + 4)(8m + 7)
b A LaTex expression showing (8m + 4)(m + 7)
8
Consolidate the shared, bracketed factors to simplify
A LaTex expression showing 5w(7w + 8) + 7(7w + 8)
a A LaTex expression showing (5w - 8)(56w + 7)
b A LaTex expression showing (7w + 8)(5w + 7)