Factor Polynomials (Order 3) - By Grouping to Order 1 Factors, Coefficient 1

Level 1

This math topic focuses on the skill of factoring third-order polynomials by grouping into first-order factors with coefficient 1. The problems present various cubic equations, each requiring the transformation into a product of linear factors (binomials). Each question provides a polynomial equation along with multiple choice solutions for the factored form. This subject area is part of an introductory unit on higher-order polynomial factoring.

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Factor Polynomials (Order 3) - By Grouping to Order 1 Factors, Coefficient 1 Worksheet

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Factor Polynomials (Order 3) - By Grouping to Order 1 Factors, Coeffi...
1
Use grouping to factor this order 3 polynomial fully
A LaTex expression showing y to the power of 3 + 2y to the power of 2 - 49y - 98
a A LaTex expression showing (y - 2)(y - 7)(y + 7)
b A LaTex expression showing (y + 2)(y - 7)(y + 7)
2
Use grouping to factor this order 3 polynomial fully
A LaTex expression showing q to the power of 3 - 9q to the power of 2 - 16q + 144
a A LaTex expression showing (q - 9)(q + 4)(q - 4)
b A LaTex expression showing (q + 9)(q + 4)(q - 4)
3
Use grouping to factor this order 3 polynomial fully
A LaTex expression showing x to the power of 3 - 6x to the power of 2 - 25x + 150
a A LaTex expression showing (x - 6)(x - 5)(x + 5)
b A LaTex expression showing (x - 6)(x + 5)(x + 5)
4
Use grouping to factor this order 3 polynomial fully
A LaTex expression showing x to the power of 3 - 6x to the power of 2 - 9x + 54
a A LaTex expression showing (x - 6)(x + 3)(x - 3)
b A LaTex expression showing (x - 6)(x + 3)(x + 3)
5
Use grouping to factor this order 3 polynomial fully
A LaTex expression showing m to the power of 3 - 2m to the power of 2 - 36m + 72
a A LaTex expression showing (m - 2)(m + 6)(m + 6)
b A LaTex expression showing (m - 2)(m - 6)(m + 6)
6
Use grouping to factor this order 3 polynomial fully
A LaTex expression showing q to the power of 3 - 6q to the power of 2 - 16q + 96
a A LaTex expression showing (q - 6)(q - 4)(q + 4)
b A LaTex expression showing (q - 6)(q + 4)(q + 4)
7
Use grouping to factor this order 3 polynomial fully
A LaTex expression showing n to the power of 3 - 4n to the power of 2 - 9n + 36
a A LaTex expression showing (n + 4)(n + 3)(n - 3)
b A LaTex expression showing (n - 4)(n + 3)(n - 3)
8
Use grouping to factor this order 3 polynomial fully
A LaTex expression showing p to the power of 3 + 4p to the power of 2 - 36p - 144
a A LaTex expression showing (p + 4)(p - 6)(p + 6)
b A LaTex expression showing (p - 4)(p - 6)(p + 6)