Question

Divide polynomial x4 – 6x3 + 8x2 + 5x - 7 by x – 1 and find quotient and remainder. Also verify the

division algorithm.​

Answer 1

Answer:

Quotient = x3 + 7x2 + 15x + 20 and Remainder = -13

Step-by-step explanation:

Check- Dividend= (Quotient * Divisor)+Remainder

So LHS= Dividend and RHS= (Quotient * Divisor)+Remainder.

Now,

LHS= x4 - 6x3 + 8x2 + 5x -7.

RHS= [(x-1)(x3+7x2+15x+20)]+(-13)

= x4 - 6x3 +8x2 + 5x + 6 + (-13)

= x4 - 6x3 + 8x2 + 5x -7 = LHS

So, RHS = LHS

Thus, Proved.

Hope it helps.