This math topic focuses on factoring quadratic equations that have a leading coefficient. The exercises involve splitting the quadratic expression into terms and finding common factors between the first two terms and the last two terms of each equation. These problems help develop skills in manipulating algebraic expressions, particularly in polynomial factoring within the context of quadratics with a leading coefficient. Each problem presents a quadratic in standard form and asks for factoring it by recognizing and extracting common factors among grouped terms.

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

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Factor the Quadratic Equation with Coefficient - Split X Terms To Par...
1
Find common factors of the first 2 and last 2 terms
A LaTex expression showing 15p to the power of 2 + 12p + 35p + 28
a A LaTex expression showing 5p(3p + 4) - 7(3p + 4)
b A LaTex expression showing 3p(5p - 4) - 7(5p - 4)
c A LaTex expression showing 3p(5p + 4) + 7(5p + 4)
d A LaTex expression showing 3p(5p + 7) - 4(5p + 7)
2
Find common factors of the first 2 and last 2 terms
A LaTex expression showing 36m to the power of 2 + 16m + 27m + 12
a A LaTex expression showing 4m(9m - 4) - 3(9m - 4)
b A LaTex expression showing 9m(4m + 4) - 3(4m + 4)
c A LaTex expression showing 4m(9m + 3) - 4(9m + 3)
d A LaTex expression showing 4m(9m + 4) + 3(9m + 4)
3
Find common factors of the first 2 and last 2 terms
A LaTex expression showing 42t to the power of 2 + 35t + 36t + 30
a A LaTex expression showing 7t(6t - 5) - 6(6t - 5)
b A LaTex expression showing 6t(7t + 5) - 6(7t + 5)
c A LaTex expression showing 7t(6t + 6) - 5(6t + 6)
d A LaTex expression showing 7t(6t + 5) + 6(6t + 5)
4
Find common factors of the first 2 and last 2 terms
A LaTex expression showing 35t to the power of 2 + 42t + 20t + 24
a A LaTex expression showing 7t(5t - 6) - 4(5t - 6)
b A LaTex expression showing 7t(5t + 6) + 4(5t + 6)
c A LaTex expression showing 5t(7t + 6) - 4(7t + 6)
d A LaTex expression showing 7t(5t + 4) - 6(5t + 4)
5
Find common factors of the first 2 and last 2 terms
A LaTex expression showing 63p to the power of 2 + 36p + 35p + 20
a A LaTex expression showing 9p(7p + 4) + 5(7p + 4)
b A LaTex expression showing 9p(7p - 4) - 5(7p - 4)
c A LaTex expression showing 9p(7p + 5) - 4(7p + 5)
d A LaTex expression showing 7p(9p + 4) - 5(9p + 4)
6
Find common factors of the first 2 and last 2 terms
A LaTex expression showing 21w to the power of 2 + 56w + 15w + 40
a A LaTex expression showing 7w(3w + 8) + 5(3w + 8)
b A LaTex expression showing 3w(7w + 8) - 5(7w + 8)
c A LaTex expression showing 7w(3w - 8) - 5(3w - 8)
d A LaTex expression showing 7w(3w + 5) - 8(3w + 5)
7
Find common factors of the first 2 and last 2 terms
A LaTex expression showing 48y to the power of 2 + 56y - 30y - 35
a A LaTex expression showing 8y(6y + 5) - 7(6y + 5)
b A LaTex expression showing 8y(6y - 7) - 5(6y - 7)
c A LaTex expression showing 8y(6y + 7) + 5(6y + 7)
d A LaTex expression showing 8y(6y + 7) - 5(6y + 7)
e A LaTex expression showing 6y(8y + 7) - 5(8y + 7)
8
Find common factors of the first 2 and last 2 terms
A LaTex expression showing 28y to the power of 2 + 21y + 36y + 27
a A LaTex expression showing 7y(4y - 3) - 9(4y - 3)
b A LaTex expression showing 7y(4y + 3) + 9(4y + 3)
c A LaTex expression showing 4y(7y + 3) - 9(7y + 3)
d A LaTex expression showing 7y(4y + 9) - 3(4y + 9)