Factor Polynomials (Order 3) - Sum of Cubes (No Hint), Coefficient N

Level 1

This topic explores the skill of factoring third-order polynomials using the sum of cubes formula. It involves recognizing the form of the polynomial and applying the sum/difference of cubes formula, \( a^3 \pm b^3 = (a \pm b)(a^2 \mp ab + b^2) \), to factorize each expression. The polynomials given are binomials with constant coefficients. Each problem presents a polynomial to factor and provides two potential factorizations (labeled as answer a and answer b). This activity tests the ability to correctly apply algebraic identities in polynomial factorization at a beginner level.

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

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Factor Polynomials (Order 3) - Sum of Cubes (No Hint), Coefficient N Worksheet

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Factor Polynomials (Order 3) - Sum of Cubes (No Hint), Coefficient N
1
Use the sum of cubes formula to factor this polynomial
A LaTex expression showing 64t to the power of 3 - 216
a A LaTex expression showing (4t + 6)(16t to the power of 2 - 24t + 36)
b A LaTex expression showing (4t - 6)(16t to the power of 2 + 24t - 36)
2
Use the sum of cubes formula to factor this polynomial
A LaTex expression showing 216n to the power of 3 - 8
a A LaTex expression showing (6n - 2)(36n to the power of 2 + 12n - 4)
b A LaTex expression showing (2n + 4)(36n to the power of 2 + 12n + 2)
3
Use the sum of cubes formula to factor this polynomial
A LaTex expression showing 125n to the power of 3 - 27
a A LaTex expression showing (5n + 125)(25n to the power of 2 - 15n + 9)
b A LaTex expression showing (5n - 3)(25n to the power of 2 + 15n - 9)
4
Use the sum of cubes formula to factor this polynomial
A LaTex expression showing 8m to the power of 3 + 8
a A LaTex expression showing (2m + 4)(4m to the power of 2 + 4m + 2)
b A LaTex expression showing (2m + 2)(4m to the power of 2 - 4m + 4)
5
Use the sum of cubes formula to factor this polynomial
A LaTex expression showing 125z to the power of 3 + 64
a A LaTex expression showing (5z + 125)(25z to the power of 2 - 20z + 16)
b A LaTex expression showing (5z + 4)(25z to the power of 2 - 20z + 16)
6
Use the sum of cubes formula to factor this polynomial
A LaTex expression showing 8m to the power of 3 + 125
a A LaTex expression showing (2m + 5)(4m to the power of 2 - 10m + 25)
b A LaTex expression showing (5m + 4)(4m to the power of 2 - 10m + 25)
7
Use the sum of cubes formula to factor this polynomial
A LaTex expression showing 64x to the power of 3 - 125
a A LaTex expression showing (4x + 5)(20x to the power of 2 - 16x + 25)
b A LaTex expression showing (4x - 5)(16x to the power of 2 + 20x - 25)
8
Use the sum of cubes formula to factor this polynomial
A LaTex expression showing 216q to the power of 3 + 64
a A LaTex expression showing (6q + 4)(36q to the power of 2 - 24q + 16)
b A LaTex expression showing (6q + 4)(24q to the power of 2 - 36q + 16)