Divide: (x^4 - 5x^2 + 2x - 7) / (x - 5)
- Thread starter adpcane15
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I'm sorry to hear that this hasn't been covered in class or in your textbook. Unfortunately, we cannot reasonably provide the requested instruction within this environment. So please consider studying a few of the many lessons available online:adpcane15 said:
. . . . .Google results for "dividing polynomials"
. . . . .Google results for "synthetic division"
Once you have studied some lessons and learned the basic terms and techniques, please attempt the exercise. If you get stuck, or are unsure of your steps or solution, please reply showing all of your work and reasoning.
Thank you!
Eliz.
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 \(\displaystyle x^3+5x^2+20x+102 + \frac{503}{x-5}\)
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 \(\displaystyle x^3+5x^2+20x+102 + \frac{503}{x-5}\)