Quadratic Equations Quiz
The question sheet
Reveal any answer as you study-
What is the process of splitting a product into factors called?
- Factoring
- Multiplying
- Grouping
- 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.
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What is the GCF of 54 and 36?
- 6
- 9
- 12
- 18
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
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What is the GCF of 4x²y and 6xy³?
- 4xy
- xy
- 2x²y
- 2xy
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 .
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What is the GCF of 21x³, 9x², and 15x?
- 21x
- 3x
- 3x²
- x
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.
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Which property is applied 'in reverse' to factor a polynomial?
- Distributive Property
- Commutative Property
- Square Root Property
- Associative 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)
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The factored form of the polynomial 4x + 12 uses which method?
- Square Root Property
- Factoring a trinomial
- Factoring out the GCF
- Factoring by grouping
Reveal answer
Answer: Factoring out the GCF
Source evidence
PDF page 819: EXAMPLE 7.5 HOW TO FACTOR THE GREATEST COMMON FACTOR FROM A POLYNOMIAL Factor: 4x + 12 . Solution
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When factoring 5a + 5, the result is:
- 5a(1)
- a(5 + 1)
- 5(a + 5)
- 5(a + 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)
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When the leading coefficient is negative, the GCF is factored as:
- A binomial
- Always 1
- A positive number
- A negative number
Reveal answer
Answer: A negative number
Source evidence
PDF page 823: When the leading coefficient is negative, we factor the negative out as part of the GCF. EXAMPLE 7.12 Factor: −8y − 24 . Solution When the leading coefficient is negative, the GCF will be negative.
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In Example 7.12, factoring −8y − 24 uses which value as the GCF?
- 4
- 8
- −24
- −8
Reveal answer
Answer: −8
Source evidence
PDF page 823: Ignoring the signs of the terms, we first find the GCF of 8y and 24 is 8. Since the expression −8y − 24 has a negative leading coefficient, we use −8 as the GCF.
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In Example 7.14, factoring 5q(q+7) − 6(q+7), the GCF is:
- The binomial q + 7
- q
- 5q
- 6
Reveal answer
Answer: The binomial q + 7
Source evidence
PDF page 824: Factor: 5q⎝q + 7⎠ − 6⎝q + 7⎠ . Solution The GCF is the binomial q + 7 .
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When a polynomial has four terms, a good first step is to:
- Add all terms together
- Separate into two parts of two terms
- Divide by 4
- Apply the Square Root Property
Reveal answer
Answer: Separate into two parts of two terms
Source evidence
PDF page 825: When there is no common factor of all the terms of a polynomial, look for a common factor in just some of the terms. When there are four terms, a good way to start is by separating the polynomial into two parts with two terms in each part. Then look for the GCF in each part. If the polynomial can be factored, you will find a common factor emerges from both parts. (Not all polynomials can be factored. Just like some numbers are prime, some polynomials are prime.)
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What is the first step in factoring by grouping?
- Group terms with common factors
- Multiply the factors
- Find the LCM
- Check the answer
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.
Elementary Algebra 2e
Elementary Algebra 2e by OpenStax, used under CC BY 4.0. Changes made by Stratacademy.
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