Q. If f(x) = x^2 - 6x + 8, what are the roots of f(x)?
A.
2 and 4
B.
1 and 8
C.
3 and 5
D.
0 and 6
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Solution
Factoring gives f(x) = (x - 2)(x - 4). Setting each factor to zero gives the roots x = 2 and x = 4.
Correct Answer:
A
— 2 and 4
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Q. What is the solution set for the equation 3x + 2 = 11?
A.
x = 3
B.
x = 4
C.
x = 5
D.
x = 2
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Solution
To solve for x, subtract 2 from both sides: 3x = 9. Then divide by 3: x = 3.
Correct Answer:
B
— x = 4
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Q. What is the solution set for the inequality x^2 - 5x + 6 > 0?
A.
x < 2 or x > 3
B.
2 < x < 3
C.
x < 3
D.
x > 2
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Solution
Factoring gives (x - 2)(x - 3) > 0. The roots are x = 2 and x = 3. The solution set is x < 2 or x > 3.
Correct Answer:
A
— x < 2 or x > 3
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Q. What is the solution to the equation 3x + 4 = 10?
A.
x = 2
B.
x = 3
C.
x = 4
D.
x = 5
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Solution
To solve for x, subtract 4 from both sides: 3x = 6. Then divide by 3: x = 2.
Correct Answer:
A
— x = 2
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Q. What is the solution to the inequality x^2 - 5x + 6 > 0?
A.
x < 2 or x > 3
B.
2 < x < 3
C.
x < 3
D.
x > 2
Show solution
Solution
Factoring gives (x - 2)(x - 3) > 0. The roots are x = 2 and x = 3. The solution set is x < 2 or x > 3.
Correct Answer:
A
— x < 2 or x > 3
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Q. What is the value of x in the equation 3x + 2 = 11?
Show solution
Solution
Subtract 2 from both sides: 3x = 9. Then divide by 3: x = 3.
Correct Answer:
A
— 3
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Q. What is the value of x in the equation 4x - 12 = 0?
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Solution
Add 12 to both sides: 4x = 12. Then divide by 4: x = 3.
Correct Answer:
A
— 3
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Q. Which of the following is a factor of the polynomial x^3 - 3x^2 - 4x + 12?
A.
x - 2
B.
x + 2
C.
x - 3
D.
x + 3
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Solution
Using synthetic division or the factor theorem, we can test x = 2. Substituting gives us 2^3 - 3(2^2) - 4(2) + 12 = 0, confirming that x - 2 is a factor.
Correct Answer:
A
— x - 2
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Q. Which of the following is a factor of the polynomial x^3 - 4x^2 + 4x?
A.
x - 2
B.
x + 2
C.
x
D.
x - 4
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Solution
We can factor out x from the polynomial: x^3 - 4x^2 + 4x = x(x^2 - 4x + 4) = x(x - 2)^2. Thus, x is a factor.
Correct Answer:
C
— x
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Q. Which of the following is a root of the polynomial x^2 + 3x - 10?
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Solution
Factoring gives (x + 5)(x - 2) = 0. The roots are x = -5 and x = 2, so 2 is a root.
Correct Answer:
B
— 2
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Q. Which of the following represents the factored form of x^2 + 7x + 10?
A.
(x + 5)(x + 2)
B.
(x + 10)(x - 1)
C.
(x - 5)(x - 2)
D.
(x + 1)(x + 10)
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Solution
To factor x^2 + 7x + 10, we look for two numbers that multiply to 10 and add to 7. The numbers 5 and 2 work, so the factored form is (x + 5)(x + 2).
Correct Answer:
A
— (x + 5)(x + 2)
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