Question 1

Which of the following is the correct definition of the Greatest Common Factor (GCF) when factoring polynomials?

Accepted Answer

The GCF is the largest factor that divides each term of a polynomial evenly.

Question 2

What is the GCF of the polynomial $$12x^3$$ + $$18x^2$$?

Accepted Answer

$$6x^2$$

Question 3

After factoring out the GCF from $$30x^3$$ - $$40x^2 - 10x$, which expression remains inside the parentheses?

Accepted Answer

$$(3x^2 - 4x - 1$$)$$

Question 4

Which of the following is the correct GCF for the polynomial $$4x^2y^2$ - 12x^2$y + 6xy^2$?

Accepted Answer

$$2xy$$

Question 5

If you factor $$-9w + 6w by $$taking out $$-3w as $$the GCF, what is the resulting expression?

Accepted Answer

$$-3w(3 - 2)$$

Question 6

Which of the following is the correct factorization of $$6x(y+2) - 5(y+2)$$?

Accepted Answer

$$(y+2)(6x - 5)$$

Question 7

A company wants to distribute $$36$$, $$42$$, and $$12$$ items equally into boxes. What is the maximum number of items that can be placed in each box if all boxes have the same number of items?

Accepted Answer

$$6$$

Question 8

What is the correct factorization by grouping for $$4a^3$$ + $$12a^2 + 7a + 21$?

Accepted Answer

$$(a+3)(4a^2 + 7$$)$$

Question 9

When factoring $$5x(y-2) + 3(y-2) by $$grouping, what is the resulting expression?

Accepted Answer

$$(y-2)(5x + 3)$$

Question 10

Which of the following is the correct factorization by grouping for $$3x^2(x+4) - 5(x+4$$)$$?

Accepted Answer

$$(x+4)(3x^2 - 5$$)$$

Question 11

If you factor $$3x(y+7) - 2(y+7) by $$grouping, what is the resulting expression?

Accepted Answer

$$(y+7)(3x - 2)$$

Question 12

Which of the following is a correct real-world application of factoring out the GCF?

Accepted Answer

Finding the largest number of identical groups that can be formed from different quantities.

Question 13

What is the GCF of $$18x^2$$ and $$32x^3$$?

Accepted Answer

$$2x^2$$

Question 14

Which of the following is the correct factorization of $$27x^2 - 9x$?

Accepted Answer

$$9x(3x - 1)$$

Question 15

If you factor $$4x^2y^2$ - 12x^2$y + 6xy^2$ by GCF, what is the expression inside the parentheses?

Accepted Answer

$$(2xy - 6y + 3y)$$

Question 16

Which of the following statements about factoring by grouping is correct?

Accepted Answer

Factoring by grouping is used when there is no common factor for all terms, but common factors exist in pairs of terms.

Question 17

When factoring $$6x(y+2) - 5(y+2)$$, which method is used?

Accepted Answer

Factoring out a common binomial

Question 18

If the first term of a polynomial is negative, what can you do to make factoring easier?

Accepted Answer

Factor out a negative GCF to change the signs of all terms.

Question 19

Which of the following is the correct factorization of $$6x(y+2) - 5(y+2)$$?

Accepted Answer

$$(y+2)(6x - 5)$$

Question 20

A medical researcher has $$36$$, $$42$$, and $$12$$ samples and wants to divide them into groups with the same number of samples. What is the largest group size possible?

Accepted Answer

$$6$$

Factoring Polynomials: GCF and Grouping Methods

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