Q. What is the factored form of the expression x^2 + 7x + 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 - 10)(x + 1)
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 factored form of the polynomial 2x^2 - 8?
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A.
2(x - 4)(x + 4)
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B.
2(x - 2)(x + 2)
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C.
2(x - 4)(x - 2)
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D.
2(x + 4)(x + 2)
Solution
Step 1: Factor out the common term: 2(x^2 - 4). Step 2: Recognize the difference of squares: 2(x - 4)(x + 4).
Correct Answer:
A
— 2(x - 4)(x + 4)
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Q. What is the factored form of the quadratic equation x^2 - 5x + 6?
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A.
(x - 2)(x - 3)
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B.
(x + 2)(x + 3)
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C.
(x - 1)(x - 6)
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D.
(x + 1)(x + 6)
Solution
Step 1: Find two numbers that multiply to 6 and add to -5: -2 and -3. Step 2: Write the factors: (x - 2)(x - 3).
Correct Answer:
A
— (x - 2)(x - 3)
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Q. What is the solution to 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: x = 4.
Correct Answer:
A
— x = 1
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Q. Which of the following is a root of the polynomial x^2 - 4?
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A.
-2
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B.
0
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C.
2
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D.
Both -2 and 2
Solution
Step 1: Factor the polynomial: (x - 2)(x + 2). Step 2: Set each factor to zero: x - 2 = 0 or x + 2 = 0. Roots are x = 2 and x = -2.
Correct Answer:
D
— Both -2 and 2
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Q. Which of the following is a solution to the equation 4x + 1 = 17?
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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 = 5
Solution
Step 1: Subtract 1 from both sides: 4x = 16. Step 2: Divide by 4: x = 4.
Correct Answer:
C
— x = 2
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