Question

Use the remainder theorem to find the remainder when f(x) is divided by x-1. Then use the factor theorem to determine whether x - 1 is a factor of f(x). f(x) = 2x⁴ + 2x³ + 2x - 6

Answer 1

To find the remainder when f(x) is divided by x-1, substitute x=1 into f(x), which gives a remainder of zero. Therefore, x-1 is a factor of f(x).

Step-by-step explanation:

To find the remainder when f(x) is divided by x-1, we can use the remainder theorem. The remainder theorem states that if we divide a polynomial f(x) by x-a, where a is a constant, the remainder is equal to f(a). So, to find the remainder when f(x) is divided by x-1, we substitute x=1 into f(x) and evaluate.

By substituting x=1 into f(x)=2x⁴+2x³+2x-6, we get f(1)=2(1)⁴+2(1)³+2(1)-6=2+2+2-6=0.

Since the remainder is zero, we can conclude that x-1 is a factor of f(x).