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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