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How to Perform Polynomial Long Division in just TEN STEPS:
A step-by-step guide
Example #1:
Find the quotient of:
Step #
Set up the division in this format:
Step #
First divide the first term of the dividend (x^2 ) by the first term of the divisor (x), and write the answer on the top line:
Step #
Now take that x, and multiply it by the divisor (x + 1) and write is directly underneath making sure to line it up with the “like” terms above it :
Step #
Now we must subtract the lined up polynomials: o (I have added the changed signs in red so now we can just add the terms)
Step #
When the terms are added the x^2 will cancel out and leave you with -10x:
Step #
Now we must carry down the -10 from the dividend to the same line as the -10x:
Step #
Now we must divide the NEW first term of the dividend (-10x) by x and write it up top of the divisor sign:
Step #
Now I'll multiply the – 10 (on top) by the divisor (x+1) and line the product up with the like terms as shown below (refer to step #3):
How to rewrite the quotient with a remainder
Some examples of polynomial division give a remainder, just as in this example below:
In this case we would write this quotient as:
x^2 – 2x + 4 +
- where the remainder is added to the solution and written as a fraction over the divisor
Check your work
you can check your work by multiplying the divisor by the quotient and then adding the remainder (if there is one) o this should give you the dividend if not…try again!
