Q. Factor the expression 3x^2 - 12.
A.
3(x^2 - 4)
B.
(3x - 6)(x + 2)
C.
3(x - 4)(x + 1)
D.
3(x - 2)(x + 2)
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Solution
First, factor out the greatest common factor, which is 3. This gives us 3(x^2 - 4). Then, x^2 - 4 can be factored as (x - 2)(x + 2). So, the complete factorization is 3(x - 2)(x + 2).
Correct Answer:
A
— 3(x^2 - 4)
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Q. Factor the expression 4x^2 - 16.
A.
4(x - 4)(x + 4)
B.
4(x^2 - 4)
C.
(2x - 4)(2x + 4)
D.
4(x - 2)(x + 2)
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Solution
First, factor out the greatest common factor, which is 4. This gives us 4(x^2 - 4). Then, x^2 - 4 can be factored as (x - 2)(x + 2). So, the complete factorization is 4(x - 2)(x + 2).
Correct Answer:
A
— 4(x - 4)(x + 4)
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Q. Factor the expression x^2 + 4x - 12.
A.
(x + 6)(x - 2)
B.
(x - 6)(x + 2)
C.
(x + 12)(x - 1)
D.
(x - 4)(x + 3)
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Solution
We need two numbers that multiply to -12 and add to 4. The numbers 6 and -2 work. Thus, the factored form is (x + 6)(x - 2).
Correct Answer:
A
— (x + 6)(x - 2)
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Q. Factor the expression: x^2 + 3x - 10
A.
(x + 5)(x - 2)
B.
(x - 5)(x + 2)
C.
(x + 10)(x - 1)
D.
(x - 10)(x + 1)
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Solution
We need two numbers that multiply to -10 and add to 3. The numbers 5 and -2 work. Thus, the factorization is (x + 5)(x - 2).
Correct Answer:
A
— (x + 5)(x - 2)
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Q. Factor the polynomial 3x^2 - 12.
A.
3(x - 4)(x + 4)
B.
3(x - 2)(x + 2)
C.
3(x + 4)(x + 4)
D.
3(x - 6)(x + 2)
Show solution
Solution
First, factor out the greatest common factor, which is 3. This gives us 3(x^2 - 4). Then, factor x^2 - 4 as a difference of squares: 3(x - 2)(x + 2).
Correct Answer:
A
— 3(x - 4)(x + 4)
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Q. Factor the quadratic expression x^2 + 7x + 10.
A.
(x + 5)(x + 2)
B.
(x - 5)(x - 2)
C.
(x + 10)(x - 1)
D.
(x - 7)(x - 10)
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Solution
We need two numbers that multiply to 10 and add to 7. The numbers 5 and 2 work. Thus, the factored form is (x + 5)(x + 2).
Correct Answer:
A
— (x + 5)(x + 2)
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Q. What is the factored form of the expression x^2 - 5x + 6?
A.
(x - 2)(x - 3)
B.
(x + 2)(x + 3)
C.
(x - 1)(x - 6)
D.
(x + 1)(x + 6)
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Solution
To factor x^2 - 5x + 6, we need two numbers that multiply to 6 and add to -5. The numbers -2 and -3 work. Thus, the factored form is (x - 2)(x - 3).
Correct Answer:
A
— (x - 2)(x - 3)
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Q. What is the factored form of the expression x^2 - 6x + 9?
A.
(x - 3)(x - 3)
B.
(x + 3)(x + 3)
C.
(x - 9)(x + 1)
D.
(x + 6)(x - 3)
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Solution
This is a perfect square trinomial. The factored form is (x - 3)(x - 3) or (x - 3)^2.
Correct Answer:
A
— (x - 3)(x - 3)
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Q. What is the factored form of the expression x^2 - 9?
A.
(x - 3)(x + 3)
B.
(x - 9)(x + 1)
C.
(x + 9)(x - 1)
D.
(x - 1)(x + 1)
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Solution
This is a difference of squares. The factored form is (x - 3)(x + 3).
Correct Answer:
A
— (x - 3)(x + 3)
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Q. Which of the following is the correct factorization of 2x^2 + 8x?
A.
2x(x + 4)
B.
2(x^2 + 4x)
C.
x(2x + 8)
D.
2x^2(1 + 4)
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Solution
First, factor out the greatest common factor, which is 2x. This gives us 2x(x + 4).
Correct Answer:
A
— 2x(x + 4)
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Q. Which of the following is the factored form of 2x^2 + 8x?
A.
2x(x + 4)
B.
2(x + 4)(x + 2)
C.
x(2x + 8)
D.
2x(x + 2)
Show solution
Solution
First, factor out the greatest common factor, which is 2x. This gives us 2x(x + 4).
Correct Answer:
A
— 2x(x + 4)
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