Factor the trinomial x^2 + 2x - 15. Which of the following choices shows the correct facto… — Armed Services Vocational Aptitude Battery (ASVAB)

Factor the trinomial $x^2 + 2x - 15$ . Which of the following choices shows the correct factorization?

The correct factorization is

(x + 5)(x - 3)

To factor the quadratic expression

x^2 + 2x - 15

, we need to find two numbers that multiply to

-15

and add up to

2

. The numbers

5

and

-3

meet these criteria (

5 \times -3 = -15

and

5 + -3 = 2

). Therefore, the completely factored form is

(x + 5)(x - 3)

Identify the target sum and product for the factors.

The target sum is the coefficient of the middle term (

2

), and the target product is the constant term (

-15

To factor a trinomial

x^2 + bx + c

into

(x + p)(x + q)

, we need to find two integers

p

and

q

that multiply to

c

and add up to

b

Find the two integers that satisfy both conditions.

The factor pairs of

-15

are

(-1, 15)

(1, -15)

(-3, 5)

, and

(3, -5)

. The pair that adds to

2

-3

and

5

Checking the sums, only

5 + (-3) = 2

provides the correct middle coefficient.

Write the factored form using the selected integers.

The factored form is

(x + 5)(x - 3)

Substituting

5

and

-3

into the binomial framework

(x + p)(x + q)

completes the factorization.

Factoring Monic Quadratic Trinomials

Question