# Algebra 1b: Unit 11 Obj 5: Factoring Trinomials

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• 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)

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).

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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)

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).

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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)

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).

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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)

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).

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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)

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.

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• 6.

### X2 + x – 90

• A.

(x – 9)(x – 10)

• B.

(x – 9)(x + 10)

• C.

(x + 9)(x – 10)

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).

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• 7.

### X2 – 6x + 8

• A.

(x – 4)(x + 2)

• B.

(x + 4)(x + 2)

• C.

(x – 4)(x – 2)

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.

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• Current Version
• Jun 21, 2023
Quiz Edited by
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• Oct 15, 2014
Quiz Created by
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