Question

Remainder Theorem question
(Screenshot included)

Answer 1

c = 5

using the Remainder Theorem.

If a polynomial f(x) is divided by (x - a) then remainder is f(a)

for (x - 2 ) → a = 2

evaluating the polynomial f(2) gives

f(2) = 2(2)³ -c(2)² +4(2) - 7 = - 3 = 16 -4c + 8 - 7 = -3 → ( solve for c )

17 - 4c = - 3 → - 4c = - 3 - 17 = - 20 ⇒ c = 5

f(x) = 2x³ -5x² + 4x - 7