Question

Use synthetic division to find the values of and y if x + 1 and x - 2 are the factors of the Polynomial x² + a * x² + ax + 6

Answer 1

The values of a and y are a = -1 and y = 8.

Given that x + 1 and x - 2 are factors of the polynomial x² + ax² + ax + 6, we can rewrite the polynomial as (x + 1)(x - 2) = x² - x - 2. By comparing the coefficients of the corresponding terms, we can equate them to find the values of a and y.

Comparing the x² terms, we have 1 + a = 0, which implies a = -1.

Comparing the constant terms, we have 6 - y = -2, which implies y = 8.

Therefore, the values of a and y are a = -1 and y = 8.