CramX Logo

Q
QuestionMathematics

Which binomial is a factor of x 2 + 2x−15?
12 months agoReport content

Answer

Full Solution Locked

Sign in to view the complete step-by-step solution and unlock all study resources.

Step 1:
I'll solve this step by step using the guidelines you specified:

Step 2:
: To find which binomial is a factor, we'll use the factor theorem.

This means we'll test potential factors by checking which values of x make the polynomial equal to zero.

Step 3:
: The potential factors of the constant term (- 15) are: ±1, ±3, ±5, ±15

Step 4:
: We'll systematically test these potential factors by substituting them into the polynomial x^{2} + 2x - 15

Step 5:
: Let's check x = 3:

3^{2} + 2(3) - 15 = 9 + 6 - 15 = 0

Step 6:
: Since 3^{2} + 2(3) - 15 = 0, (x - 3) is a factor of the polynomial.

Step 7:
: We can verify by polynomial long division or by factoring:

x^{2} + 2x - 15 = (x - 3)(x + 5)

Final Answer

The binomial (x - 3) is a factor of x^{2} + 2x - 15.