Question 1

Given the polynomial

$\frac{1}{5}x^4 + \frac{4}{5}x^6 - \frac{6}{5}x^5 + \frac{1}{5}x$

factor out the greatest common factor (GCF). What is the factored form?

Accepted Answer

$\frac{1}{5}x(x^3 + 4x^5 - 6x^4 + 1)$

Question 2

Which of the following is the GCF (Greatest Common Factor) of the terms in the polynomial

$\frac{1}{5}x^4 + \frac{4}{5}x^6 - \frac{6}{5}x^5 + \frac{1}{5}x$?

Accepted Answer

$\frac{1}{5}x$

Question 3

After factoring out the GCF from the polynomial

$\frac{1}{5}x^4 + \frac{4}{5}x^6 - \frac{6}{5}x^5 + \frac{1}{5}x$

what is the coefficient of the $x^5$ term inside the parentheses?

Accepted Answer

$4$

Question 4

If you factor $\frac{1}{5}x$ from $\frac{4}{5}x^6$, what is the resulting term inside the parentheses?

Accepted Answer

$4x^5$

Question 5

Which of the following steps is correct when factoring $\frac{1}{5}x$ from $-\frac{6}{5}x^5$?

Accepted Answer

$-6x^4$

Question 6

Which of the following is NOT a correct step in factoring the GCF from the polynomial $\frac{1}{5}x^4 + \frac{4}{5}x^6 - \frac{6}{5}x^5 + \frac{1}{5}x$?

Accepted Answer

Leaving the polynomial unchanged

Question 7

If you expand $\frac{1}{5}x(x^3 + 4x^5 - 6x^4 + 1)$, what is the coefficient of $x^6$ in the resulting polynomial?

Accepted Answer

$4$

Question 8

Which of the following polynomials is equivalent to $\frac{1}{5}x^4 + \frac{4}{5}x^6 - \frac{6}{5}x^5 + \frac{1}{5}x$ after factoring out the GCF?

Accepted Answer

$\frac{1}{5}x(x^3 + 4x^5 - 6x^4 + 1)$

Question 9

Which of the following best describes the process of factoring out the GCF from a polynomial?

Accepted Answer

Finding the largest expression that divides all terms and writing the polynomial as a product

Question 10

A chemist is analyzing a formula that can be written as $\frac{1}{5}x^4 + \frac{4}{5}x^6 - \frac{6}{5}x^5 + \frac{1}{5}x$. To simplify calculations, she wants to factor out the GCF. What expression should she use for further calculations?

Accepted Answer

$\frac{1}{5}x(x^3 + 4x^5 - 6x^4 + 1)$

Factoring Out the Greatest Common Factor (GCF) from a Polynomial

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