Q. Factor the expression 2x^2 + 8x + 6.
-
A.
2(x + 3)(x + 1)
-
B.
2(x + 2)(x + 3)
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C.
2(x + 1)(x + 3)
-
D.
2(x + 4)(x + 1)
Solution
First, factor out the common term 2: 2(x^2 + 4x + 3). Then, factor the quadratic: 2(x + 3)(x + 1).
Correct Answer:
A
— 2(x + 3)(x + 1)
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Q. Factor the expression 2x^2 - 8.
-
A.
2(x - 4)(x + 4)
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B.
2(x - 2)(x + 2)
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C.
2(x - 4)
-
D.
x(2x - 8)
Solution
To factor 2x^2 - 8, first factor out 2: 2(x^2 - 4). Then, recognize x^2 - 4 as a difference of squares: 2(x - 2)(x + 2).
Correct Answer:
A
— 2(x - 4)(x + 4)
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Q. Factor the expression 4x^2 - 12x + 9.
-
A.
(2x - 3)(2x - 3)
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B.
(2x + 3)(2x + 3)
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C.
(4x - 3)(x - 3)
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D.
(2x - 1)(2x - 9)
Solution
The expression 4x^2 - 12x + 9 is also a perfect square trinomial. It factors to (2x - 3)(2x - 3) or (2x - 3)^2.
Correct Answer:
A
— (2x - 3)(2x - 3)
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Q. Factor the expression x^2 - 4.
-
A.
(x - 2)(x + 2)
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B.
(x - 4)(x + 4)
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C.
(x + 4)(x + 2)
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D.
(x - 1)(x + 1)
Solution
The expression x^2 - 4 is a difference of squares. It factors to (x - 2)(x + 2).
Correct Answer:
A
— (x - 2)(x + 2)
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Q. Factor the polynomial 2x^2 - 8.
-
A.
2(x - 4)(x + 4)
-
B.
2(x - 2)(x + 2)
-
C.
2(x - 4)
-
D.
x(2x - 8)
Solution
Factor out the common term 2: 2(x^2 - 4) = 2(x - 2)(x + 2).
Correct Answer:
A
— 2(x - 4)(x + 4)
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Q. Factor the polynomial x^3 - 3x^2 - 4x.
-
A.
x(x^2 - 3x - 4)
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B.
x(x + 4)(x - 1)
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C.
x^2(x - 3) - 4
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D.
x(x^2 + 4)
Solution
First, factor out the common term x: x(x^2 - 3x - 4). Now, factor the quadratic x^2 - 3x - 4 to get x(x - 4)(x + 1).
Correct Answer:
A
— x(x^2 - 3x - 4)
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Q. Factor the quadratic expression x^2 - 5x + 6.
-
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
To factor x^2 - 5x + 6, we need two numbers that multiply to 6 and add to -5. The numbers -2 and -3 work. Thus, the factorization is (x - 2)(x - 3).
Correct Answer:
A
— (x - 2)(x - 3)
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Q. Solve the equation 2x^2 - 8 = 0.
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A.
x = 2
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B.
x = -2
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C.
x = 4
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D.
x = -4
Solution
First, add 8 to both sides: 2x^2 = 8. Then divide by 2: x^2 = 4. Finally, take the square root: x = ±2, so the solutions are x = 2 and x = -2.
Correct Answer:
C
— x = 4
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Q. Solve the equation 3x + 7 = 16.
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A.
x = 3
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B.
x = 2
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C.
x = 1
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D.
x = 4
Solution
To solve 3x + 7 = 16, subtract 7 from both sides: 3x = 9. Then divide by 3: x = 3.
Correct Answer:
A
— x = 3
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Q. Solve the inequality 3x - 7 < 2.
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A.
x < 3
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B.
x < 2
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C.
x > 3
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D.
x > 2
Solution
To solve 3x - 7 < 2, add 7 to both sides: 3x < 9. Then divide by 3: x < 3.
Correct Answer:
A
— x < 3
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Q. What is the factored form of 2x^2 + 8x?
-
A.
2x(x + 4)
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B.
2(x + 4)(x + 2)
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C.
2x(x + 2)
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D.
x(2x + 8)
Solution
First, factor out the common term 2x from 2x^2 + 8x. This gives us 2x(x + 4).
Correct Answer:
A
— 2x(x + 4)
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Q. What is the factored form of x^2 + 4x + 4?
-
A.
(x + 2)(x + 2)
-
B.
(x - 2)(x - 2)
-
C.
(x + 4)(x + 1)
-
D.
(x - 4)(x - 1)
Solution
This is a perfect square trinomial. It factors to (x + 2)(x + 2) or (x + 2)^2.
Correct Answer:
A
— (x + 2)(x + 2)
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Q. What is the factored form of x^2 + 6x + 9?
-
A.
(x + 3)(x + 3)
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B.
(x - 3)(x - 3)
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C.
(x + 2)(x + 4)
-
D.
(x + 1)(x + 9)
Solution
The expression x^2 + 6x + 9 is a perfect square trinomial. It factors to (x + 3)(x + 3) or (x + 3)^2.
Correct Answer:
A
— (x + 3)(x + 3)
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Q. What is the solution set for the inequality x + 2 > 3?
-
A.
x > 1
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B.
x < 1
-
C.
x > 5
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D.
x < 5
Solution
To solve x + 2 > 3, subtract 2 from both sides: x > 1.
Correct Answer:
A
— x > 1
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Q. What is the solution set for the inequality x + 5 > 2?
-
A.
x > -3
-
B.
x < -3
-
C.
x > 3
-
D.
x < 3
Solution
To solve x + 5 > 2, subtract 5 from both sides: x > -3.
Correct Answer:
A
— x > -3
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Q. What is the solution to the inequality 5x + 3 > 2x + 12?
-
A.
x < 3
-
B.
x > 3
-
C.
x < -3
-
D.
x > -3
Solution
Subtract 2x from both sides: 3x + 3 > 12. Then subtract 3: 3x > 9. Finally, divide by 3: x > 3.
Correct Answer:
B
— x > 3
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Q. What is the solution to the inequality x + 5 > 2?
-
A.
x > -3
-
B.
x < -3
-
C.
x > 3
-
D.
x < 3
Solution
Subtract 5 from both sides: x > -3.
Correct Answer:
A
— x > -3
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