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Question
Divide x2−9x−10byx+1. Write down all steps involved in division.
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Solution
Divide x2−9x−10byx+1
First,1 set up the divisionx+1√x2−9x−10For the moment,I′ll ignore the other terms and look just at the leading x of the divisor and the leading x2 of the divided If I divide the leading x2 inside by the leading x inxx+1√x2−9x−10front, what would I get? I′d get an x.SoI′ll put an x on top Now I′ll take that x, and multiply it through thexx+1√x2−9x−10x2divisor,x+1.First,Imultiply then x(on top)by the x(on the "side"),and carry the x2 underneath: Then I′ll multiply the x (on top) by the 1(on the "side")xx+1√x2−9x−10x2+1xand carry the 1x undermeath: Then I′ll draw the "equals"bar,so I can do the subtractionxx+1√x2−9x−10−x2∓1x To subtract the polynomials,I change all the signs in the second line … and then I add down.The first term (the x2)will cancel out:xx+1√x2−9x−10−x2∓1x−10xI need to remember to carry down that last term,xx+1√x2−9x−10−x2∓1x−10x−10the "subtract ten",from the dividend: Now I look at the x from the divisor and the newx−10x+q√x2−9x−10−x2∓1x−10x−10leading term,the−10x,in the bottom line of the division If I divide the −10x by the x,I would end up with a−10, so I′ll put that on top: Now,I′ll multiply the−10(on top)by the leading xx−10x+1√x2−9x−10−x2∓1x−10x−10−10x(on the "side"),and carry the−10x to the bottom …and I′ll multiply the −10(on top)by the 1 (on the "side"),x−10x+1√x2−9x−10−x2∓1x−10x−10−10x−10and carry the−10 to the bottom: I draw the equals bar,and change the signsx−10x+1√x2−9x−10−x2∓1x−10x−10+10x+10the terms in the bottom row: Then I add down:x−10x+1√x2−9x−10−x2∓1x−10x−10+10x+100
Then the solution to this division is : x-10
Divide x2−9x−10byx+1
First,1 set up the divisionx+1√x2−9x−10For the moment,I′ll ignore the other terms and look just at the leading x of the divisor and the leading x2 of the divided If I divide the leading x2 inside by the leading x inxx+1√x2−9x−10front, what would I get? I′d get an x.SoI′ll put an x on top Now I′ll take that x, and multiply it through thexx+1√x2−9x−10x2divisor,x+1.First,Imultiply then x(on top)by the x(on the "side"),and carry the x2 underneath: Then I′ll multiply the x (on top) by the 1(on the "side")xx+1√x2−9x−10x2+1xand carry the 1x undermeath: Then I′ll draw the "equals"bar,so I can do the subtractionxx+1√x2−9x−10−x2∓1x To subtract the polynomials,I change all the signs in the second line … and then I add down.The first term (the x2)will cancel out:xx+1√x2−9x−10−x2∓1x−10xI need to remember to carry down that last term,xx+1√x2−9x−10−x2∓1x−10x−10the "subtract ten",from the dividend: Now I look at the x from the divisor and the newx−10x+q√x2−9x−10−x2∓1x−10x−10leading term,the−10x,in the bottom line of the division If I divide the −10x by the x,I would end up with a−10, so I′ll put that on top: Now,I′ll multiply the−10(on top)by the leading xx−10x+1√x2−9x−10−x2∓1x−10x−10−10x(on the "side"),and carry the−10x to the bottom …and I′ll multiply the −10(on top)by the 1 (on the "side"),x−10x+1√x2−9x−10−x2∓1x−10x−10−10x−10and carry the−10 to the bottom: I draw the equals bar,and change the signsx−10x+1√x2−9x−10−x2∓1x−10x−10+10x+10the terms in the bottom row: Then I add down:x−10x+1√x2−9x−10−x2∓1x−10x−10+10x+100
Then the solution to this division is : x-10
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