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

Level 1

This math topic focuses on practicing the skill of factoring third-order polynomials by grouping to find common factors, with a coefficient of 1. It delves into this technique by providing multiple problems where students must pair terms and factor out a common factor as the initial step in the polynomial factoring process. Each problem includes a polynomial expression and potential answers, indicating a structured approach to reach the factored form. This skill is introduced as an introductory unit on higher-order polynomial factoring.

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 Common Factors, Coefficient 1 Worksheet

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Factor Polynomials (Order 3) - By Grouping to Common Factors, Coeffic...
1
Group the terms in pairs and remove a common factor to begin factoring by grouping
A LaTex expression showing n to the power of 3 + 4n to the power of 2 + 5n + 20
a A LaTex expression showing n to the power of 2 (n - 4) - 30(n - 4)
b A LaTex expression showing n to the power of 2 (n + 4) + 5(n + 4)
2
Group the terms in pairs and remove a common factor to begin factoring by grouping
A LaTex expression showing y to the power of 3 - 9y to the power of 2 + 2y - 18
a A LaTex expression showing y to the power of 2 (y - 9) - 16(y - 9)
b A LaTex expression showing y to the power of 2 (y - 9) + 2(y - 9)
3
Group the terms in pairs and remove a common factor to begin factoring by grouping
A LaTex expression showing q to the power of 3 + 3q to the power of 2 + 6q + 18
a A LaTex expression showing q to the power of 2 (q + 3) - 42(q + 3)
b A LaTex expression showing q to the power of 2 (q + 3) + 6(q + 3)
4
Group the terms in pairs and remove a common factor to begin factoring by grouping
A LaTex expression showing t to the power of 3 + 9t to the power of 2 + 2t + 18
a A LaTex expression showing t to the power of 2 (t + 9) + 2(t + 9)
b A LaTex expression showing t to the power of 2 (t - 9) - 14(t - 9)
5
Group the terms in pairs and remove a common factor to begin factoring by grouping
A LaTex expression showing q to the power of 3 + 3q to the power of 2 + 8q + 24
a A LaTex expression showing q to the power of 2 (q + 3) + 8(q + 3)
b A LaTex expression showing q to the power of 2 (q - 3) + 16(q - 3)
6
Group the terms in pairs and remove a common factor to begin factoring by grouping
A LaTex expression showing w to the power of 3 - 4w to the power of 2 - 9w + 36
a A LaTex expression showing w to the power of 2 (w - 4) - 9(w - 4)
b A LaTex expression showing w to the power of 2 (w + 4) - 9(w + 4)
7
Group the terms in pairs and remove a common factor to begin factoring by grouping
A LaTex expression showing r to the power of 3 - 2r to the power of 2 + 7r - 14
a A LaTex expression showing r to the power of 2 (r - 2) - 56(r - 2)
b A LaTex expression showing r to the power of 2 (r - 2) + 7(r - 2)
8
Group the terms in pairs and remove a common factor to begin factoring by grouping
A LaTex expression showing t to the power of 3 - 8t to the power of 2 + 2t - 16
a A LaTex expression showing t to the power of 2 (t - 8) + 2(t - 8)
b A LaTex expression showing t to the power of 2 (t - 44) + 12(t - 44)