Question

Determine whether the second polynomial is a factor of the first: 6x²+ 5x + 35; x - 2.

Options:
Option 1: Yes
Option 2: No

Answer 1

The remainder theorem states that if the polynomial 6x² + 5x + 35 is divided by x - 2, the remainder is 69, indicating that x - 2 is not a factor.

Step-by-step explanation:

To determine whether the second polynomial is a factor of the first, we can use the remainder theorem. The remainder theorem states that if the polynomial p(x) is divided by x - a, then the remainder is equal to p(a). In this case, we have the polynomial 6x² + 5x + 35 and the divisor x - 2. We can substitute 2 into the polynomial to check if the remainder is 0. Evaluating, we get 6(2)² + 5(2) + 35 = 24 + 10 + 35 = 69. Since the remainder is not 0, the second polynomial is not a factor of the first.