To find the remainder of the polynomial 2x³ + 4x² + 32x + 18 when divided by x – 3, we can use the Remainder Theorem. This theorem states that the remainder of a polynomial f(x) when divided by x – a is simply f(a).
In this case, a = 3. So, we will evaluate the polynomial at x = 3.
Let’s calculate:
- f(3) = 2(3)³ + 4(3)² + 32(3) + 18
- = 2(27) + 4(9) + 32(3) + 18
- = 54 + 36 + 96 + 18
- = 204
Thus, the remainder when 2x³ + 4x² + 32x + 18 is divided by x – 3 is 204.