Question

Find the remainder when f(x) = 2x³ + 2x² – 3x – 3 is divided by x - 2.

A. 11
B.-5
C. 71
D. 15

Answer 1

The remainder when the polynomial f(x) = 2x³ + 2x² – 3x – 3 is divided by x - 2 is found using the Remainder Theorem, which gives us a result of 15, corresponding to option D.

Step-by-step explanation:

To find the remainder when the polynomial f(x) = 2x³ + 2x² – 3x – 3 is divided by x - 2, we can use synthetic division or apply the Remainder Theorem, which states that the remainder of the division of a polynomial by a linear divisor (x - r) is equal to f(r). In this case, we substitute x = 2 into the polynomial.

Using the Remainder Theorem, we evaluate f(2):

f(2) = 2(2)³ + 2(2)² – 3(2) – 3
= 2(8) + 2(4) – 6 – 3
= 16 + 8 – 6 – 3
= 24 – 6 – 3
= 18 – 3
= 15

Therefore, the remainder is 15, which corresponds to option D.