Question

The remainder when the expression x^3+6x^2+x+c is divided by x-2 is twice the remainder when the expression is divided by x-1.

show that c=24

Answer 1

• c = 18

Explanation:

According to the remainder theorem, the remainder when f(x) is divided by (x - n) is f(n).

As per question we are given:

• f(2) = 2f(1)

Substitute and solve for c:

• 2³ + 6*2² + 2 + c = 2(1³ + 6*1² + 1 + c)
• 8 + 24 + 2 + c = 2(1 + 6 + 1 + c)
• 34 + c = 2(8 + c)
• 34 + c = 16 + 2c
• 2c - c = 34 - 16
• c = 18

Note: I got a different value of c. This may be a result of a typo in the given expression. I provided a guide to solve such problems. Let me know is anything is unclear.