What is the quotient and the remainder when #x^4 — 2x^2 +3x - 1# is divided by #x+1#?

1 Answer
EZ as pi
Jun 22, 2016

#x^3 -x^2 -x +4" " rem -5#

Explanation:

#f(x) = x^4 + 0x^3 -2x^2 +3x -1#

FOr the remainder: find #f(-1)#

#f(-1) = (-1)^4 + 0(-1)^3 -2(-1)^2 +3(-1) -1 = -5#

The remainder is -5.

By synthetic division:

Write the coefficients of the expression - include 0 for #x^3#

"the format does not work so well - (follow the method below)
Apart from the first 1, all the numbers in the last row have to be multiplied by -1"

#"1 0 -2 +3 -1"#
# " -1 +1 1 -4 "#

#"1 -1 -1 4 -5"#

Bring down the first 1.
Multiply it by-1 and write the answer under the second number (0).
Add, to get -1.
Multiply -1 by-1 and write the answer under the third number (-2)
Add to get -1
Multiply -1 by-1 and write the answer under the fourth number (3)
Add to get 4.
Multiply 4 by-1 and write the answer under the fifth number (-1)

Add to get -5. This is the remainder.

Each of the numbers in the last row is a coefficient of the terms in descending powers of #x#.

Quotient is: #x^3 -x^2 -x +4" " rem -5#

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