Divide: (x^4 - 5x^2 + 2x - 7) / (x - 5)
Sorry. I can't figure out how to space properly. It is a "long division" problem. Set it up like this.
......_______________________
x-5 ) x^4 + 0x^3 - 5x^2 + 2x - 7
Divide 1st term of dividend by 1st term of divisor... x^4 divided by x = x^3. This will be the 1st term of the dividend.
........x^3_____________________
x-5 ) x^4 + 0x^3 - 5x^2 + 2x - 7
Multiply 1st term of quotient times entire divisor and place in proper columns beneath the dividend. (x^3)(x-5)=x^4 - 5x^3.
........x^3____________________
x-5 ) x^4 + 0x^3 - 5x^2 + 2x - 7
........x^4 - 5x^3
subtract
........x^3______________________
x-5 ) x^4 + 0x^3 - 5x^2 + 2x - 7
........x^4 - 5x^3
.................+5x^3
Bring down next term.
........x^3_____________________
x-5 ) x^4 + 0x^3 - 5x^2 + 2x - 7
........x^4 - 5x^3
................+ 5x^3 - 5x^2
Now divide 1st term of this remainder by 1st term of divisor. 5x^3 divided by x = 5x^2. This is second term of quotient.
........x^3 + 5x^2_________________
x-5 ) x^4 + 0x^3 - 5x^2 + 2x - 7
........x^4 - 5x^3
................+ 5x^3 - 5x^2
Etc.
You should wind up with a quotient of
x3+5x2+20x+102+x−5503