This math topic involves practicing the factorization of quadratic equations with a leading coefficient, in standard form. The problems emphasize the skill of splitting the middle term into two terms that sum to the middle coefficient and multiply to the product of the first and last coefficients of the quadratic equation. Each question provides the equation and multiple-choice answers where this split has been performed differently. The objective is to understand and apply the correct method for factoring quadratic expressions by recognizing and creating pairs of numbers that fulfill specific conditions related to the 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 - Standard Form To Split X Terms Worksheet

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Factor the Quadratic Equation with Coefficient - Standard Form To Spl...
1
Split the 'n' terms into terms that add to the middle coefficient and multiply to (first * last) coefficients
A LaTex expression showing 25n to the power of 2 + 5n - 6
a A LaTex expression showing 25n to the power of 2 + 15n + 6n + 10
b A LaTex expression showing 25n to the power of 2 + 15n - 10n - 6
c A LaTex expression showing 25n to the power of 2 - 15n - 10n + 6
d A LaTex expression showing 25n to the power of 2 + 15n - 10n + 6
e A LaTex expression showing 15n to the power of 2 + 25n + 10n + 6
2
Split the 'x' terms into terms that add to the middle coefficient and multiply to (first * last) coefficients
A LaTex expression showing 6x to the power of 2 + 17x + 12
a A LaTex expression showing 6x to the power of 2 - 8x + 9x + 12
b A LaTex expression showing 6x to the power of 2 - 8x - 9x + 12
c A LaTex expression showing 6x to the power of 2 + 8x + 9x + 12
d A LaTex expression showing 6x to the power of 2 + 8x - 9x + 12
e A LaTex expression showing 6x to the power of 2 + 8x + 12x + 9
3
Split the 'w' terms into terms that add to the middle coefficient and multiply to (first * last) coefficients
A LaTex expression showing 4w to the power of 2 + 24w + 35
a A LaTex expression showing 4w to the power of 2 - 14w + 10w + 35
b A LaTex expression showing 4w to the power of 2 + 14w + 10w + 35
c A LaTex expression showing 4w to the power of 2 + 14w + 35w + 10
d A LaTex expression showing 4w to the power of 2 + 14w - 10w + 35
e A LaTex expression showing 4w to the power of 2 - 14w - 10w + 35
4
Split the 'w' terms into terms that add to the middle coefficient and multiply to (first * last) coefficients
A LaTex expression showing 8w to the power of 2 + 22w + 15
a A LaTex expression showing 10w to the power of 2 + 8w + 12w + 15
b A LaTex expression showing 8w to the power of 2 + 10w - 12w + 15
c A LaTex expression showing 8w to the power of 2 - 10w + 12w + 15
d A LaTex expression showing 8w to the power of 2 + 10w + 12w + 15
e A LaTex expression showing 8w to the power of 2 + 10w + 15w + 12
5
Split the 'y' terms into terms that add to the middle coefficient and multiply to (first * last) coefficients
A LaTex expression showing 10y to the power of 2 - 3y - 18
a A LaTex expression showing 10y to the power of 2 + 12y + 18y + 15
b A LaTex expression showing 10y to the power of 2 + 12y - 15y - 18
c A LaTex expression showing 12y to the power of 2 + 10y + 15y + 18
d A LaTex expression showing 10y to the power of 2 - 12y + 15y + 18
e A LaTex expression showing 10y to the power of 2 + 12y - 15y + 18
6
Split the 'r' terms into terms that add to the middle coefficient and multiply to (first * last) coefficients
A LaTex expression showing 18r to the power of 2 + 23r - 6
a A LaTex expression showing 27r to the power of 2 + 18r + 4r + 6
b A LaTex expression showing 18r to the power of 2 - 27r + 4r + 6
c A LaTex expression showing 18r to the power of 2 + 27r + 6r + 4
d A LaTex expression showing 18r to the power of 2 + 27r - 4r + 6
e A LaTex expression showing 18r to the power of 2 + 27r - 4r - 6
7
Split the 'z' terms into terms that add to the middle coefficient and multiply to (first * last) coefficients
A LaTex expression showing 15z to the power of 2 + 1z - 6
a A LaTex expression showing 15z to the power of 2 - 10z + 9z + 6
b A LaTex expression showing 15z to the power of 2 - 10z - 9z + 6
c A LaTex expression showing 10z to the power of 2 + 15z + 9z + 6
d A LaTex expression showing 15z to the power of 2 + 10z - 9z - 6
e A LaTex expression showing 15z to the power of 2 + 10z - 9z + 6
8
Split the 'x' terms into terms that add to the middle coefficient and multiply to (first * last) coefficients
A LaTex expression showing 28x to the power of 2 + 29x + 6
a A LaTex expression showing 28x to the power of 2 - 21x + 8x + 6
b A LaTex expression showing 28x to the power of 2 + 21x + 8x + 6
c A LaTex expression showing 28x to the power of 2 + 21x + 6x + 8
d A LaTex expression showing 28x to the power of 2 - 21x - 8x + 6
e A LaTex expression showing 28x to the power of 2 + 21x - 8x + 6