What is the remainder when the polynomial 2x⁴ - 3x² + 5x - 7 is divided by x + 2?
What is the remainder when the polynomial 2x⁴ - 3x² + 5x - 7 is divided by x + 2?
Explanation
To find the remainder, we can use the Remainder Theorem, which states that the remainder of a polynomial f(x) divided by x - a is f(a). In this case, we need to divide by x + 2, so we'll use x = -2.
f(x) = 2x⁴ - 3x² + 5x - 7
f(-2) = 2(-2)⁴ - 3(-2)² + 5(-2) - 7
= 2(16) - 3(4) - 10 - 7
= 32 - 12 - 10 - 7
= 32 - 29
= 3