To find the GCF, the first step is to:

Factor each coefficient into primes

What is the first step in factoring by grouping?

Group terms with common factors

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Greatest Common Factor and Factor by Grouping Quiz

12 questions math Grades 7-8

The question sheet

Reveal any answer as you study

01
What is splitting a product into factors called?
- Factoring
- Multiplying
- Rounding
- Distributing
Reveal answer

Answer: Factoring

Source evidence
PDF page 816: Earlier we multiplied factors together to get a product. Now, we will be reversing this process; we will start with a product and then break it down into its factors. Splitting a product into factors is called factoring.
02
According to Example 7.1, what is the GCF of 54 and 36?
- 9
- 18
- 12
- 6
Reveal answer

Answer: 18

Source evidence
PDF page 817: Notice that, because the GCF is a factor of both numbers, 54 and 36 can be written as multiples of 18.
PDF page 817: 54 = 18 · 3 36 = 18 · 2
03
In Example 7.3, what is the GCF of 4x^2y and 6xy^3?
- 2x^2y
- 2xy
- 4xy
- 6xy
Reveal answer

Answer: 2xy

Source evidence
PDF page 818: Bring down the common factors. Multiply the factors. 2 The GCF of 4x y and 3 6xy is 2xy .
04
In Example 7.4, what is the GCF of 21x^3, 9x^2, and 15x?
- 3x^2
- x
- 3x
- 3
Reveal answer

Answer: 3x

Source evidence
PDF page 818: Bring down the common factors. Multiply the factors. 3 2 The GCF of 21x , 9x and 15x is 3x.
05
To find the GCF, the first step is to:
- Factor each coefficient into primes
- Circle the largest term
- Multiply the factors
- List all variables
Reveal answer

Answer: Factor each coefficient into primes

Source evidence
PDF page 817: Step 1. Factor each coefficient into primes. Write all variables with exponents in expanded form. Step 2. List all factors—matching common factors in a column. In each column, circle the common factors. Step 3. Bring down the common factors that all expressions share. Step 4. Multiply the factors.
06
Which property is applied 'in reverse' to factor a polynomial?
- Associative Property
- Distributive Property
- Commutative Property
- Subtraction Property
Reveal answer

Answer: Distributive Property

Source evidence
PDF page 819: The form on the left is used to multiply. The form on the right is used to factor. So how do you use the Distributive Property to factor a polynomial? You just find the GCF of all the terms and write the polynomial as a product!
PDF page 819: a(b + c) = ab + ac and ab + ac = a(b + c)
07
According to the Distributive Property, ab + ac equals:
- (a + b)c
- abc
- a(b + c)
- a + b + c
Reveal answer

Answer: a(b + c)

Source evidence
PDF page 819: a(b + c) = ab + ac and ab + ac = a(b + c)
08
In Example 7.6, factoring 5a + 5 gives:
- 5(a + 5)
- a(5 + 1)
- 5(a + 1)
- 5a(1)
Reveal answer

Answer: 5(a + 1)

Source evidence
PDF page 820: Rewrite each term as a product using the GCF. Use the Distributive Property "in reverse" to factor the GCF. Check by mulitplying the factors to get the orginal polynomial. 5(a + 1)
09
In Example 7.7, factoring 12x − 60 gives:
- 6(2x − 10)
- x(12 − 60)
- 12(x − 60)
- 12(x − 5)
Reveal answer

Answer: 12(x − 5)

Source evidence
PDF page 820: Rewrite each term as a product using the GCF. Factor the GCF. Check by mulitplying the factors. 12(x − 5)
10
In Example 7.13, factoring −6a^2 + 36a gives:
- 6a(a − 6)
- 6a(a + 6)
- −6a(a − 6)
- −6a(a + 6)
Reveal answer

Answer: −6a(a − 6)

Source evidence
PDF page 824: Rewrite each term using the GCF. Factor the GCF. Check. −6a(a − 6)
11
In Example 7.14, what is the common factor in 5q(q+7) − 6(q+7)?
- q + 7
- q
- 6
- 5q
Reveal answer

Answer: q + 7

Source evidence
PDF page 824: Factor: 5q⎝q + 7⎠ − 6⎝q + 7⎠ . Solution The GCF is the binomial q + 7 .
12
What is the first step in factoring by grouping?
- Group terms with common factors
- Check by multiplying
- Add all terms
- Factor out the common factor
Reveal answer

Answer: Group terms with common factors

Source evidence
PDF page 825: Step 1. Group terms with common factors. Step 2. Factor out the common factor in each group. Step 3. Factor the common factor from the expression. Step 4. Check by multiplying the factors.