Question

Find the remainder when f(x) = 2x3 – 12x2 + 11x + 2 is divided by x – 5.

Answer:
A) 3
B) –7
C) 7
D) –3

Answer 1

To find the remainder when the function f(x) is divided by x - 5, we use the Remainder Theorem and substitute 5 into the function. The calculation leads to a remainder of 7.

Step-by-step explanation:

To find the remainder when the function f(x) = 2x3 − 12x2 + 11x + 2 is divided by x − 5, you can use the Remainder Theorem. This theorem states that the remainder of a polynomial f(x) divided by x − a is f(a). So, in this case, we need to evaluate f(5).

Substituting 5 for x in the function:
f(5) = 2(5)3 − 12(5)2 + 11(5) + 2
= 2(125) − 12(25) + 55 + 2
= 250 − 300 + 55 + 2
= 7.

Therefore, the remainder when f(x) is divided by x − 5 is 7, which corresponds to option C.

Answer 2

The remainder of the function divided by a factor can be obtained by substituting the factor to the function. In this case, we substitute 5 to the x in the expression 2x3 – 12x2 + 11x + 2. The answer is equal to 7. The answer hence to this problem is C