Q. What is the factored form of x^2 + 7x + 10?
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A.
(x + 5)(x + 2)
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B.
(x + 10)(x - 1)
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C.
(x - 5)(x - 2)
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D.
(x + 1)(x + 10)
Solution
Step 1: Find two numbers that multiply to 10 and add to 7: 5 and 2. Step 2: Write in factored form: (x + 5)(x + 2).
Correct Answer:
A
— (x + 5)(x + 2)
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Q. What is the result of (x + 2)(x - 2)?
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A.
x^2 - 4
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B.
x^2 + 4
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C.
2x
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D.
x^2 + 2
Solution
Step 1: Recognize this as a difference of squares: (a + b)(a - b) = a^2 - b^2. Step 2: Here, a = x and b = 2. Result is x^2 - 4.
Correct Answer:
A
— x^2 - 4
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Q. What is the value of x in the equation 3(x + 2) = 2(x + 5)?
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A.
x = 1
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B.
x = 2
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C.
x = 3
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D.
x = 4
Solution
Step 1: Distribute: 3x + 6 = 2x + 10. Step 2: Subtract 2x from both sides: x + 6 = 10. Step 3: Subtract 6 from both sides: x = 4.
Correct Answer:
A
— x = 1
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Q. What is the value of x in the equation 4x + 5 = 2x + 17?
Solution
Step 1: Subtract 2x from both sides: 2x + 5 = 17. Step 2: Subtract 5 from both sides: 2x = 12. Step 3: Divide by 2: x = 6.
Correct Answer:
A
— 3
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