Question

If two polynomial ax³+4x²+3x-4 & x³-4x+a leave the same remainder when divided by (x-3), find the value of a.​

Answer 1

Answer:

       a = -1

Step-by-step explanation:

The Remainder Theorem says that when a polynomial f(x) is divided by x-a, the remainder is f(a).

So dividing ax³ + 4x² + 3x - 4 by x-3 leaves the remainder

• a×3³ + 4×3² + 3×3 - 4  =  27a + 36 + 9 - 4  =  27a + 41

and dividing x³ - 4x + a by x-3 leaves the remainder

• 3³ - 4×3 + a  =  27 - 12 + a  =  a + 15.

Since the remainders are the same,

     27a + 41  =  a + 15

⇒  26a = -26

⇒  a = -1