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

Level 1

This math topic involves practicing the skill of factoring third-order polynomials by grouping them into first-order factors with coefficients of one. Each problem presents a polynomial and its purported factors, and the task is to determine whether the provided factoring is correct. The format is true/false, where students must choose between 'Yes' and 'No' responses to affirm whether the factoring given is accurate. This exercise is meant to strengthen students' understanding of polynomial factoring within the broader subject of higher order 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 to Order 1 Factors, Coefficient 1 (True/False) Worksheet

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Factor Polynomials (Order 3) - By Grouping to Order 1 Factors, Coeffi...
1
A LaTex expression showing q to the power of 3 + 4q to the power of 2 - 9q - 36\\=(q + 4)(q - 3)(q + 3)
Is this factoring step correct?
a
Yes
b
No
2
A LaTex expression showing x to the power of 3 - 8x to the power of 2 - 16x + 128\\=(x - 8)(x - 4)(x - 4)
Is this factoring step correct?
a
No
b
Yes
3
A LaTex expression showing r to the power of 3 - 3r to the power of 2 - 25r + 75\\=(r - 3)(r + 5)(r + 5)
Is this factoring step correct?
a
No
b
Yes
4
A LaTex expression showing t to the power of 3 - 7t to the power of 2 - 16t + 112\\=(t - 7)(t + 4)(t + 4)
Is this factoring step correct?
a
No
b
Yes
5
A LaTex expression showing q to the power of 3 - 9q to the power of 2 - 9q + 81\\=(q + 9)(q - 3)(q - 3)
Is this factoring step correct?
a
No
b
Yes
6
A LaTex expression showing x to the power of 3 + 3x to the power of 2 - 16x - 48\\=(x - 3)(x + 4)(x + 4)
Is this factoring step correct?
a
No
b
Yes
7
A LaTex expression showing z to the power of 3 - 9z to the power of 2 - 9z + 81\\=(z - 9)(z - 3)(z + 3)
Is this factoring step correct?
a
Yes
b
No
8
A LaTex expression showing w to the power of 3 + 9w to the power of 2 - 9w - 81\\=(w - 9)(w - 3)(w + 3)
Is this factoring step correct?
a
No
b
Yes