ranwei12345
Answered

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 :

mhanifa

Answer:

  • c = 18

Step-by-step 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.

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