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

Level 1

This math topic focuses on factoring third-order polynomials primarily through identifying and factoring out common binomial factors. It offers a series of problems that involve rewriting polynomials as products of simpler factors by consolidating shared common factors into binomial factors. The exercise emphasizes the need to manipulate algebraic expressions to recognize patterns and simplify them into a product of polynomials, enhancing algebraic skills in polynomial factorization.

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, Common Factors to Order 2 Factors, Coefficient 1 Worksheet

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Factor Polynomials (Order 3) - By Grouping, Common Factors to Order 2...
1
Consolidate the shared common factor to create 2 binomial factors
A LaTex expression showing t to the power of 2 (t - 6) - 25(t - 6)
a A LaTex expression showing (t + 6)(t to the power of 2 - 150)
b A LaTex expression showing (t - 6)(t to the power of 2 - 25)
2
Consolidate the shared common factor to create 2 binomial factors
A LaTex expression showing p to the power of 2 (p - 2) + 6(p - 2)
a A LaTex expression showing (p - 2)(p to the power of 2 + 6)
b A LaTex expression showing (p + 2)(p to the power of 2 - 12)
3
Consolidate the shared common factor to create 2 binomial factors
A LaTex expression showing z to the power of 2 (z + 2) + 3(z + 2)
a A LaTex expression showing (z + 2)(z to the power of 2 + 3)
b A LaTex expression showing (z + 2)(z to the power of 2 - 3)
4
Consolidate the shared common factor to create 2 binomial factors
A LaTex expression showing z to the power of 2 (z - 3) + 6(z - 3)
a A LaTex expression showing (z - 3)(z to the power of 2 + 6)
b A LaTex expression showing (z + 3)(z to the power of 2 + 6)
5
Consolidate the shared common factor to create 2 binomial factors
A LaTex expression showing r to the power of 2 (r - 6) + 5(r - 6)
a A LaTex expression showing (r + 6)(r to the power of 2 + 5)
b A LaTex expression showing (r - 6)(r to the power of 2 + 5)
6
Consolidate the shared common factor to create 2 binomial factors
A LaTex expression showing n to the power of 2 (n - 9) + 3(n - 9)
a A LaTex expression showing (n - 9)(n to the power of 2 + 3)
b A LaTex expression showing (n + 9)(n to the power of 2 + 3)
7
Consolidate the shared common factor to create 2 binomial factors
A LaTex expression showing r to the power of 2 (r - 2) + 7(r - 2)
a A LaTex expression showing (r + 2)(r to the power of 2 - 7)
b A LaTex expression showing (r - 2)(r to the power of 2 + 7)
8
Consolidate the shared common factor to create 2 binomial factors
A LaTex expression showing w to the power of 2 (w - 9) - 9(w - 9)
a A LaTex expression showing (w + 9)(w to the power of 2 + 9)
b A LaTex expression showing (w - 9)(w to the power of 2 - 9)