How do you divide #(x^3 - 2x^2 - 4x + 5) /( x - 3)#?

Question

Avery Alexander · Accepted Answer

The solution of the expression is: #x^2+x-1+2/(x-3)#.

At first rewrite the expression into this form: #(x^3-2x^2-4x+5)#:#(x-3) =# We will divide the term of the first polynomial by the first term in the second polynomial: #(x^3-2x^2-4x+5)#:#(x-3) =x^2# , because #x^3/x=x^2# Now we will multiply the second polynomial by our first term of the result and deduct it from the first polynomial: #(x^3-2x^2-4x+5)-x^2*(x-3)=x^2-4x+5# We have a new polynomial #x^2-4x+5# and we have to do the same as in the first step: #(x^2-4x+5)#:#(x-3)=x# Now multiply and deduct: #(x^2-4x+5)-(x-3)*x=-x+5# #(-x+5)#:#(x-3)=-1# #(-x+5)-(x-3)*(-1)=2# The last term of the polynomial will be divided by the entire second polynomial: #2/(x-3)# The final result is the sum of each result: #x^2+x-1+2/(x-3)#

Ethan Adkins · Answer

undefined To divide (x^3 - 2x^2 - 4x + 5) by (x - 3), we can use long division.

First, divide x^3 by x, which gives us x^2. Multiply (x - 3) by x^2, which gives us x^3 - 3x^2. Subtract this from the original polynomial to get (-x^2 - 4x + 5).

Next, divide -x^2 by x, which gives us -x. Multiply (x - 3) by -x, which gives us -x^2 + 3x. Subtract this from the previous result to get (-7x + 5).

Now, divide -7x by x, which gives us -7. Multiply (x - 3) by -7, which gives us -7x + 21. Subtract this from the previous result to get (-16).

Since we have no more terms to divide, the final result is x^2 - x - 7 with a remainder of -16.