How do you divide #(x^4 + 2x^3 +3x -1) /(x^2+2)#?

Question

Avery Alexander · Accepted Answer

Using the distribution method, you can expand the expression.

#(x^4+2x^3+3x-1)/(x^2+2)# distribute the #(x^4+2x^3+3x-1)# to #x^2# and #2# and now we get: #(x^4+2x^3+3x-1)/x^2 + (x^4+2x^3+3x-1)/2# we can further distribute #x^2# and #2# to #(x^4+2x^3+3x-1)#: #(x^4/x^2##+##(2x^3)/x^2##+##(3x)/x^2##-##1/x^2)##+##((x^4)/2##+##(2x^3)/2##+##(3x)/2##-##1/2)# This is the simplified version: #x^2+2x+3/x-1/x^2+x^4/2+x^3+1.5x-1/2# I apologize, but I'm not sure what you're looking for, so I can only respond with this information.

Jameson Allen · Answer

undefined To divide (x^4 + 2x^3 + 3x - 1) by (x^2 + 2), you can use long division.

First, divide the highest degree term of the numerator (x^4) by the highest degree term of the denominator (x^2). This gives x^2.

Next, multiply the entire denominator (x^2 + 2) by the result from the previous step (x^2), and subtract the result from the numerator (x^4 + 2x^3 + 3x - 1). This gives you a new polynomial: (2x^3 + 3x - 1 - x^2(x^2 + 2)). Simplifying further, you get (2x^3 + 3x - 1 - x^4 - 2x^2).

Repeat the process by dividing the highest degree term of the new polynomial (2x^3) by the highest degree term of the denominator (x^2). This gives you 2x.

Multiply the entire denominator (x^2 + 2) by the result from the previous step (2x), and subtract the result from the new polynomial (2x^3 + 3x - 1 - 2x(x^2 + 2)). Simplifying further, you get (3x - 1 - 2x^3 - 4x).

Continue this process until you have no more terms to divide. In this case, the final result is (x^2 + 2x - 1).