Q. Factor the expression: 2x^2 + 8x
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A.
2x(x + 4)
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B.
2(x^2 + 4x)
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C.
x(2x + 8)
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D.
2x(x + 2)
Solution
The expression 2x^2 + 8x can be factored by taking out the common factor 2x, resulting in 2x(x + 4).
Correct Answer:
A
— 2x(x + 4)
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Q. Factor the expression: 3x^2 - 12
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A.
3(x - 2)(x + 2)
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B.
3(x - 4)(x + 1)
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C.
3(x + 4)(x - 1)
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D.
3(x - 3)(x + 3)
Solution
The expression 3x^2 - 12 can be factored by taking out the common factor 3, resulting in 3(x^2 - 4), which further factors to 3(x - 2)(x + 2).
Correct Answer:
A
— 3(x - 2)(x + 2)
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Q. Factor the expression: 4x^2 - 25
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A.
(2x - 5)(2x + 5)
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B.
(4x - 5)(4x + 5)
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C.
(2x + 5)(2x + 5)
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D.
(4x + 5)(4x - 5)
Solution
The expression 4x^2 - 25 is a difference of squares, which factors to (2x - 5)(2x + 5).
Correct Answer:
A
— (2x - 5)(2x + 5)
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Q. Factor the expression: x^2 + 3x - 10
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A.
(x + 5)(x - 2)
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B.
(x - 5)(x + 2)
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C.
(x + 10)(x - 1)
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D.
(x - 3)(x + 4)
Solution
The expression x^2 + 3x - 10 factors to (x + 5)(x - 2) since 5 and -2 add to 3 and multiply to -10.
Correct Answer:
A
— (x + 5)(x - 2)
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Q. Factor the expression: x^2 + 5x + 6
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A.
(x + 2)(x + 3)
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B.
(x + 1)(x + 6)
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C.
(x - 2)(x - 3)
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D.
(x + 3)(x + 2)
Solution
The expression x^2 + 5x + 6 factors to (x + 2)(x + 3) since 2 and 3 add to 5 and multiply to 6.
Correct Answer:
A
— (x + 2)(x + 3)
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Q. Factor the expression: x^2 + 7x + 10
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A.
(x + 5)(x + 2)
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B.
(x + 1)(x + 10)
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C.
(x - 5)(x - 2)
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D.
(x + 10)(x - 1)
Solution
The expression x^2 + 7x + 10 factors to (x + 5)(x + 2) since 5 and 2 add to 7 and multiply to 10.
Correct Answer:
A
— (x + 5)(x + 2)
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Q. Factor the expression: x^2 - 4x + 4
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A.
(x - 2)(x - 2)
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B.
(x + 2)(x + 2)
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C.
(x - 4)(x + 1)
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D.
(x + 4)(x - 1)
Solution
The expression x^2 - 4x + 4 is a perfect square trinomial and factors to (x - 2)(x - 2) or (x - 2)^2.
Correct Answer:
A
— (x - 2)(x - 2)
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Q. Factor the expression: x^2 - 6x + 9
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A.
(x - 3)(x - 3)
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B.
(x + 3)(x + 3)
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C.
(x - 9)(x + 1)
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D.
(x + 6)(x - 3)
Solution
The expression x^2 - 6x + 9 is a perfect square trinomial and factors to (x - 3)(x - 3) or (x - 3)^2.
Correct Answer:
A
— (x - 3)(x - 3)
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Q. Factor the expression: x^2 - 9
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A.
(x - 3)(x + 3)
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B.
(x - 9)(x + 1)
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C.
(x - 1)(x + 9)
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D.
(x + 3)(x + 3)
Solution
The expression x^2 - 9 is a difference of squares, which factors to (x - 3)(x + 3).
Correct Answer:
A
— (x - 3)(x + 3)
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