Q. What is the factored form of the polynomial x^2 - 16?
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A.
(x - 4)(x + 4)
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B.
(x - 8)(x + 2)
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C.
(x - 2)(x + 2)
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D.
(x - 4)(x - 4)
Solution
This is a difference of squares: x^2 - 4^2 = (x - 4)(x + 4).
Correct Answer:
A
— (x - 4)(x + 4)
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Q. What is the solution to the equation x^2 + 4x + 4 = 0?
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A.
x = -2
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B.
x = 2
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C.
x = 0
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D.
x = -4
Solution
Step 1: Factor the equation: (x + 2)(x + 2) = 0. Step 2: Set the factor to zero: x + 2 = 0. Step 3: Solution is x = -2.
Correct Answer:
A
— x = -2
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Q. What is the value of x in the equation 4(x - 1) = 2x + 6?
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A.
x = 2
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B.
x = 3
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C.
x = 4
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D.
x = 5
Solution
Distribute: 4x - 4 = 2x + 6. Subtract 2x from both sides: 2x - 4 = 6. Add 4: 2x = 10. Divide by 2: x = 5.
Correct Answer:
B
— x = 3
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Q. What is the value of x in the equation 5x + 2 = 3x + 10?
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A.
x = 4
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B.
x = 3
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C.
x = 2
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D.
x = 1
Solution
Step 1: Subtract 3x from both sides: 2x + 2 = 10. Step 2: Subtract 2 from both sides: 2x = 8. Step 3: Divide by 2: x = 4.
Correct Answer:
A
— x = 4
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Q. Which of the following is the solution set for the inequality 2x + 3 > 7?
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A.
x < 2
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B.
x > 2
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C.
x < 3
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D.
x > 3
Solution
Step 1: Subtract 3 from both sides: 2x > 4. Step 2: Divide by 2: x > 2.
Correct Answer:
B
— x > 2
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