1 Select the correct answer. When using the inspection method, which number would you add to (and subtract from ) the constant term of the numerator in this expression so the polynomial in the numerator will have (x+4) as a factor? (x^(2)+7x+15)/(x+4) A. 3 B. 4 C. 7 D. 12 Reset Next
Step By Step Answers with Explanation
To find the correct number to add to and subtract from the constant term of the numerator in the expression (x^2 + 7x + 15)/(x + 4) so that the polynomial in the numerator has (x + 4) as a factor using the inspection method, we need to perform the following steps:
The factors of 15 are: 1, 3, 5, and 15.
We need to find two numbers from these factors that add up to 7. The pair of numbers that satisfies this condition is 5 and 3 because 5 + 3 = 8.
Now factor out the greatest common factor (GCF) from each pair:
x(x + 5) + 3(x + 5) = 0
Solve for x in each equation:
For x + 5 = 0: x = -5
(x^2 + 7x + 15 + 4 - 4)/(x + 4)
Now, you can simplify: