How do you divide #(-x^3 - x^2-6x+5 )/((-x + 10 )#?

Question

How do you divide #(-x^3 - x^2-6x+5 )/((-x + 10  )#?

Eva Adamson · Accepted Answer

#(−x^3−x^2−6x+5)/(-x+10)# is

#x^2+11x+116-1155/(-x+10)# To divide #−x^3−x^2−6x+5# by #-x+10#, first we observe that #-x# goes #(-x^3)/-x=x^2# times in #-x^3#. Hence, #x^2(-x+10)-10x^2−x^2−6x+5# or (note we have added and subtracted #10x^2) #x^2(-x+10)-11x^2−6x+5# As #-11x^2/-x=11x#, above can be written is #x^2(-x+10)+11x(-x+10)-110x−6x+5# or #x^2(-x+10)+11x(-x+10)-116x+5# and as #-116x/-x=116#, above can be written as #x^2(-x+10)+11x(-x+10)+116x(-x+10)-1160+5# or #x^2(-x+10)+11x(-x+10)+116x(-x+10)-1155# or #(x^2+11x+116)(-x+10)-1155# or Hence #(−x^3−x^2−6x+5)/(-x+10)# is #x^2+11x+116-1155/(-x+10)#

Genesis Allen · Answer

undefined To divide (-x^3 - x^2 - 6x + 5) by (-x + 10), you can use long division. Here are the steps:

1. Start by dividing the first term of the numerator (-x^3) by the first term of the denominator (-x). This gives you x^2 as the first term of the quotient.

2. Multiply the entire denominator (-x + 10) by x^2, which gives you (-x^3 + 10x^2).

3. Subtract this result (-x^3 + 10x^2) from the numerator (-x^3 - x^2 - 6x + 5). This gives you (-11x^2 - 6x + 5) as the new numerator.

4. Repeat the process by dividing the first term of the new numerator (-11x^2) by the first term of the denominator (-x). This gives you 11x as the next term of the quotient.

5. Multiply the entire denominator (-x + 10) by 11x, which gives you (-11x^2 + 110x).

6. Subtract this result (-11x^2 + 110x) from the new numerator (-11x^2 - 6x + 5). This gives you (-116x + 5) as the new numerator.

7. Divide the first term of the new numerator (-116x) by the first term of the denominator (-x). This gives you 116 as the next term of the quotient.

8. Multiply the entire denominator (-x + 10) by 116, which gives you (-116x + 1160).

9. Subtract this result (-116x + 1160) from the new numerator (-116x + 5). This gives you (-1155) as the final remainder.

Therefore, the quotient is x^2 + 11x + 116, and the remainder is -1155.