How do you divide #(5x^2-2x+4)/(x-1)#?

Question

Eli Assouline · Accepted Answer

#5x+3+7/(x-1)# #(5x^2-2x+4)/(x-1)# #color(white)(....,,......)5x+3# #x-1|overline(5x^2-2x+4)# #color(white)(............)ul(5x^2-5x)# #color(white)(.....................)3x+4# #color(white)(..........,,......)ul(3x-3)# #color(white)(............................)7# #(5x^2-2x+4) / (x-1) = 5x+3+7/(x-1)#

Eli Assouline · Answer

undefined To divide (5x^2-2x+4) by (x-1), you can use long division or synthetic division. Here is the solution using long division:

5x + 3
    _______________
x - 1 | 5x^2 - 2x + 4
         - (5x^2 - 5x)
         _____________
                    3x + 4
                    - (3x + 3)
                    ___________
                              1

Therefore, the quotient is 5x + 3 and the remainder is 1.

Abigail Allen · Answer

undefined To divide $ \frac{{5x^2 - 2x + 4}}{{x - 1}} $, you can use polynomial long division or synthetic division. Here's the process:

Step 1: Divide the first term of the numerator by the first term of the denominator to get the first term of the quotient.
Step 2: Multiply the entire denominator by the first term of the quotient.
Step 3: Subtract the result from the numerator.
Step 4: Repeat steps 1-3 with the result obtained until the degree of the remainder is less than the degree of the denominator.

Applying these steps will give you the quotient and the remainder.