Algebra 1b: Unit 11 Obj 5: Factoring Trinomials
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This Algebra 1B quiz focuses on factoring trinomials, assessing the learner's ability to factor quadratic expressions of the form x2 + bx + c. It includes problems like x2 + 8x + 15 and x2 + x - 90, enhancing skills crucial for algebra proficiency.
- 1.
Factor: x2 + 8x + 15
- A.
(x + 5)(x + 3)
- B.
(x - 5)(x - 3)
- C.
(x + 15)(x + 1)
- D.
(x + 5)(x - 3)
Correct Answer
A. (x + 5)(x + 3)Explanation
The given expression can be factored as (x + 5)(x + 3). This can be determined by finding two numbers that multiply to give 15 (the constant term) and add up to give 8 (the coefficient of the x term). In this case, the numbers are 5 and 3. Therefore, the correct answer is (x + 5)(x + 3).Rate this question:
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- 2.
Factor: x2 + 3x - 10
- A.
(x + 2)(x + 5)
- B.
(x + 5)(x - 2)
- C.
(x - 5)(x - 2)
- D.
(x - 5)(x + 2)
Correct Answer
B. (x + 5)(x - 2)Explanation
The given expression is a quadratic trinomial in the form of ax^2 + bx + c. To factor it, we need to find two numbers that multiply to give c (in this case, -10) and add up to give b (in this case, 3). The numbers that satisfy these conditions are 5 and -2. Therefore, the correct factorization is (x + 5)(x - 2).Rate this question:
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- 3.
Factor: x2 - 4x - 12
- A.
(x + 4)(x - 3)
- B.
(x - 4)(x + 3)
- C.
(x + 6)(x - 2)
- D.
(x - 6)(x + 2)
Correct Answer
D. (x - 6)(x + 2)Explanation
The given expression is a quadratic trinomial in the form of ax^2 + bx + c. To factorize it, we need to find two numbers whose product is equal to c (in this case, -12) and whose sum is equal to b (in this case, -4). The numbers -6 and 2 satisfy these conditions because -6 * 2 = -12 and -6 + 2 = -4. Therefore, the correct factorization is (x - 6)(x + 2).Rate this question:
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- 4.
Factor: x2 - 8x + 15
- A.
(x - 3)(x - 5)
- B.
(x + 3)(x + 5)
- C.
(x - 3)(x + 5)
- D.
(x + 3)(x - 5)
Correct Answer
A. (x - 3)(x - 5)Explanation
The given expression is a quadratic trinomial in the form of ax^2 + bx + c. To factorize it, we need to find two binomials in the form of (x + p)(x + q) that multiply to give the original expression. In this case, we can see that -3 and -5 are the two numbers that add up to -8 (the coefficient of x) and multiply to give 15 (the constant term). Therefore, the correct answer is (x - 3)(x - 5).Rate this question:
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- 5.
X2 - x - 2
- A.
(x - 1)(x - 2)
- B.
(x + 3)(x - 1)
- C.
(x - 2)(x + 1)
- D.
(x + 1)(x - 3)
Correct Answer
C. (x - 2)(x + 1)Explanation
The given expression can be factored as (x - 2)(x + 1). This can be determined by using the distributive property to expand the expression (x - 2)(x + 1) and simplifying it to x^2 - x - 2. Therefore, (x - 2)(x + 1) is the correct answer.Rate this question:
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- 6.
X2 + x – 90
- A.
(x – 9)(x – 10)
- B.
(x – 9)(x + 10)
- C.
(x + 9)(x – 10)
Correct Answer
B. (x – 9)(x + 10)Explanation
The given expression is a quadratic trinomial. To factorize it, we need to find two numbers that multiply to give the constant term (-90) and add up to give the coefficient of the middle term (1). The numbers that satisfy this condition are 9 and -10. Therefore, the correct factorization of the expression is (x - 9)(x + 10).Rate this question:
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- 7.
X2 – 6x + 8
- A.
(x – 4)(x + 2)
- B.
(x + 4)(x + 2)
- C.
(x – 4)(x – 2)
Correct Answer
C. (x – 4)(x – 2)Explanation
The given expression can be factored as (x - 4)(x - 2). This can be determined by using the distributive property to expand the expression (x - 4)(x - 2) and then simplifying it to x^2 - 6x + 8. Therefore, (x - 4)(x - 2) is the correct answer.Rate this question:
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Jun 21, 2023Quiz Edited by
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Oct 15, 2014Quiz Created by
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