Question

Divide x4 -5x2 -4x by x+3.Find the remainder by Remainder theorem. Verify by finding the remainder using Synthetic Division.​

Answer 1

Answer:

Clearly, the degree of remainder 8 is zero, which is less than the degree of x2 - x + 1.

Quotient = x2 + x - 3 and remainder = 8.

Verification:

Divisor Quotient + Reminder = (x2 - x + 1) (x2 + x - 3) + 8

= x4 + x3 - 3x2 - x3 - x2 + 3x + x2 + x - 3 + 8

= x4 + x3- x3 - 3x2 - x2 + x2 + 3x + x -3 +8

= x4 - 3x2 + 4x + 5 = dividend