Find the remainder when x^3 – 4x^3 + 12x – 45 is divided by (x – 2)?

Question

a. Find the remainder when x³ – 4x³ + 12x – 45 is divided by (x – 2)? 

b. Find the value of k if the remainder is zero on dividing 2x³ + 4x²  – 10x + k by (x – 1)

Answer 1

a. p(x) = x³ – 4x² – 12x – 45 

remainder = p(2) = 2³ – 4(2)² + 12 x 2 – 45 

= 32 – 61 = –29

b. p(x) = 2x³ + 4x² – 10x + k; p(l) = 0

\(\Rightarrow\) 2 x 13 + 4 x 12 – 10 x 1 + k = 0

2 + 4 – 10 + k = 0 – 4 + k = 0; k = 4