Question

What should be added to 5x³ + 5x - 6x² - 3 to make it exactly divisible by 5x - 1?​

Answer 1

Answer:

5x³ + 5x - 6x²

=> 5x³ - 6x² + 5x

Let us add k,

Now, p (x) 5x³ - 6x² + 5x + k

It is divisible by 5x - 1

Substitute x = 1/5, hence p (1/5) = 0

» 5 (1/5)³ - 6 (1/5)² + 5 (1/5) + k = 0

» 1/25 -6/25 + 1 + k = 0

» k = 1/5 - 1

» k = -4/5