Algebra 1b: Unit 11 Obj 5: Factoring Trinomials

1. Factor: x² + 8x + 15

(x + 5)(x + 3)

(x - 5)(x - 3)

(x + 15)(x + 1)

(x + 5)(x - 3)

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).

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).

2. Factor: x² - 8x + 15

(x - 3)(x - 5)

(x + 3)(x + 5)

(x - 3)(x + 5)

(x + 3)(x - 5)

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).

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).

3. Factor: x² + 3x - 10

(x + 2)(x + 5)

(x + 5)(x - 2)

(x - 5)(x - 2)

(x - 5)(x + 2)

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).

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).

4. X² – 6x + 8

(x – 4)(x + 2)

(x + 4)(x + 2)

(x – 4)(x – 2)

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.

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.

5. X² - x - 2

(x - 1)(x - 2)

(x + 3)(x - 1)

(x - 2)(x + 1)

(x + 1)(x - 3)

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.

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.

6. X²+ x – 90

(x – 9)(x – 10)

(x – 9)(x + 10)

(x + 9)(x – 10)

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).

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).

7. Factor: x² - 4x - 12

(x + 4)(x - 3)

(x - 4)(x + 3)

(x + 6)(x - 2)

(x - 6)(x + 2)

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).

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).