Question

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)

Answer 1

To find the number to add and subtract from the constant term of the numerator in the expression (x^2 + 7x + 15)/(x+4) so it has (x+4) as a factor, we solve the equation x+4 = 0. The solution is x = -4.

Step-by-step explanation:

When using the inspection method to find a factor of a polynomial, we need to determine a number that makes the polynomial evaluate to zero when substituted into it. In this case, we want to find a number that makes the expression (x² + 7x + 15)/(x+4) equal to zero. To do this, we need to find a value of x that satisfies the equation x+4 = 0.

We can solve this equation by subtracting 4 from both sides: x = -4. Therefore, the number we need to add to (and subtract from) the constant term of the numerator in the given expression in order to have (x+4) as a factor is -4.