Question

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

Answer 1

The value of 'a' in the given polynomial would need to be -1, and 'y' equates to 6 for the polynomial to match the product of its factors, (x + 1)(x - 2).

Step-by-step explanation:

The question appears to contain a typo and seems to relate to finding the coefficients of a quadratic polynomial that can be factored as (x + 1)(x - 2). If 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. However, the part ax² suggests a third-degree polynomial, which may be a typo as the given factors indicate a quadratic equation. Assuming the equation should be x² + ax + 6, then a would need to be -1 for the polynomial to equal x² - x - 2. Therefore, a = -1 and by equating the constant terms, y = 6.