This math topic focuses on the skill of factoring quadratic equations with a leading coefficient. Specifically, the tasks involve splitting quadratic expressions of the form ax² + bx + c into terms by finding two numbers that add up to the middle coefficient 'b' and multiply to the product of the first and last coefficients 'ac'. The problems are presented in a progressive format, challenging the learner to apply this technique to factorize different quadratic expressions involving various variables ('p', 't', 'm', 'r', 'q'). Each question is designed to reinforce understanding through practical application of polynomial factoring concepts.

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 - Standard Form To Split X Terms Worksheet

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Factor the Quadratic Equation with Coefficient - Standard Form To Spl...
1
Split the 'p' terms into terms that add to the middle coefficient and multiply to (first * last) coefficients
A LaTex expression showing 24p to the power of 2 + 25p + 6
a A LaTex expression showing 24p to the power of 2 + 9p + 16p + 6
b A LaTex expression showing 24p to the power of 2 + 9p + 6p + 16
2
Split the 't' terms into terms that add to the middle coefficient and multiply to (first * last) coefficients
A LaTex expression showing 3t to the power of 2 + 17t + 10
a A LaTex expression showing 3t to the power of 2 + 15t + 2t + 10
b A LaTex expression showing 3t to the power of 2 - 15t - 2t + 10
3
Split the 'm' terms into terms that add to the middle coefficient and multiply to (first * last) coefficients
A LaTex expression showing 9m to the power of 2 + 30m + 16
a A LaTex expression showing 9m to the power of 2 + 6m + 24m + 16
b A LaTex expression showing 6m to the power of 2 + 9m + 24m + 16
4
Split the 'm' terms into terms that add to the middle coefficient and multiply to (first * last) coefficients
A LaTex expression showing 6m to the power of 2 + 29m + 28
a A LaTex expression showing 6m to the power of 2 + 8m + 21m + 28
b A LaTex expression showing 6m to the power of 2 - 8m + 21m + 28
5
Split the 'r' terms into terms that add to the middle coefficient and multiply to (first * last) coefficients
A LaTex expression showing 2r to the power of 2 + 13r + 21
a A LaTex expression showing 2r to the power of 2 + 6r + 7r + 21
b A LaTex expression showing 2r to the power of 2 + 6r + 21r + 7
6
Split the 'q' terms into terms that add to the middle coefficient and multiply to (first * last) coefficients
A LaTex expression showing 2q to the power of 2 + 17q + 35
a A LaTex expression showing 2q to the power of 2 + 10q + 7q + 35
b A LaTex expression showing 10q to the power of 2 + 2q + 7q + 35
7
Split the 'm' terms into terms that add to the middle coefficient and multiply to (first * last) coefficients
A LaTex expression showing 5m to the power of 2 + 14m + 8
a A LaTex expression showing 5m to the power of 2 + 10m + 8m + 4
b A LaTex expression showing 5m to the power of 2 + 10m + 4m + 8
8
Split the 'y' terms into terms that add to the middle coefficient and multiply to (first * last) coefficients
A LaTex expression showing 12y to the power of 2 + 28y + 15
a A LaTex expression showing 12y to the power of 2 + 18y + 10y + 15
b A LaTex expression showing 12y to the power of 2 - 18y + 10y + 15