Factor Polynomials (Order 3) - By Grouping to Order 2 Factors, Coefficient 1

Level 1

This math topic focuses on the technique of factoring third-order (cubic) polynomials by grouping into second-order (quadratic) factors, specifically when the leading coefficient is one. It is an introductory part of a larger unit on factoring higher-order polynomials. The problems present different cubic polynomials, challenging learners to factor them by grouping to simplify the expression. Each problem provides multiple-choice answers, allowing for practice in selecting the correct factorization by recognizing patterns and applying grouping strategies effectively.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Factor Polynomials (Order 3) - By Grouping to Order 2 Factors, Coefficient 1 Worksheet

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Factor Polynomials (Order 3) - By Grouping to Order 2 Factors, Coeffi...
1
Use grouping to remove a factor from this order 3 polynomial
A LaTex expression showing m to the power of 3 + 3m to the power of 2 + 2m + 6
a A LaTex expression showing (m - 3)(m to the power of 2 - 2)
b A LaTex expression showing (m + 3)(m to the power of 2 + 2)
2
Use grouping to remove a factor from this order 3 polynomial
A LaTex expression showing t to the power of 3 + 8t to the power of 2 + 2t + 16
a A LaTex expression showing (t + 8)(t to the power of 2 + 2)
b A LaTex expression showing (t - 8)(t to the power of 2 + 2)
3
Use grouping to remove a factor from this order 3 polynomial
A LaTex expression showing p to the power of 3 - 2p to the power of 2 + 8p - 16
a A LaTex expression showing (p - 2)(p to the power of 2 + 8)
b A LaTex expression showing (p + 2)(p to the power of 2 + 34)
4
Use grouping to remove a factor from this order 3 polynomial
A LaTex expression showing x to the power of 3 - 3x to the power of 2 + 6x - 18
a A LaTex expression showing (x - 3)(x to the power of 2 + 6)
b A LaTex expression showing (x + 3)(x to the power of 2 - 18)
5
Use grouping to remove a factor from this order 3 polynomial
A LaTex expression showing y to the power of 3 - 3y to the power of 2 + 2y - 6
a A LaTex expression showing (y - 3)(y to the power of 2 + 2)
b A LaTex expression showing (y + 3)(y to the power of 2 - 2)
6
Use grouping to remove a factor from this order 3 polynomial
A LaTex expression showing w to the power of 3 - 3w to the power of 2 + 7w - 21
a A LaTex expression showing (w - 3)(w to the power of 2 + 7)
b A LaTex expression showing (w + 3)(w to the power of 2 - 21)
7
Use grouping to remove a factor from this order 3 polynomial
A LaTex expression showing q to the power of 3 + 9q to the power of 2 + 6q + 54
a A LaTex expression showing (q + 9)(q to the power of 2 + 6)
b A LaTex expression showing (q + 9)(q to the power of 2 + 54)
8
Use grouping to remove a factor from this order 3 polynomial
A LaTex expression showing r to the power of 3 + 6r to the power of 2 + 2r + 12
a A LaTex expression showing (r + 6)(r to the power of 2 + 4)
b A LaTex expression showing (r + 6)(r to the power of 2 + 2)