How do you divide #(-x^4-4x^3-9x^2-7x-7)/(x-2) #?

Answer 1

#-x^3-6x^2-21x-49# with a remainder of #-105#

On this, we can perform long division:

#color(white)((x-2)/color(black)(x-2)(-x^4-4x^3-9x^2-7x-7)/color(black)(")"bar(-x^4-4x^3-9x^2-7x-7)))#
We multiply #x# by #-x^3# to get to #-x^4#, and so we have:
#color(white)((x-2)/color(black)(x-2)(-x^4color(black)(color(white)(00)-x^3)-9x^2-7x-7)/color(black)(")"bar(-x^4-4x^3-9x^2-7x-7)))# #color(white)((x-2)/(x-2)((color(black)(-x^4+2x^3)-9x^2-7x-7)/(color(black)bar(0x^4-6x^3-9x^2)-7x-7)))#
We multiply #x# by #-6x^2# to get to #-6x^3# and so we have:
#color(white)((x-2)/color(black)(x-2)(-x^4color(black)(color(white)(00)-x^3-6x^2)-7x-7)/color(black)(")"bar(-x^4-4x^3-9x^2-7x-7)))# #color(white)((x-2)/(x-2)((color(black)(-x^4+2x^3)-9x^2-7x-7)/(color(black)bar(0x^4-6x^3-9x^2)-7x-7)))# #color(white)((x-2)/(x-2)((color(black)(color(white)(-x^4)-6x^3+12x^2)-7x-7)/(color(black)bar(color(white)(0x^4-)0x^3-21x^2-7x)-7)))#
We multiply #x# by #-21x# to get to #-21x^2# and so we have:
#color(white)((x-2)/color(black)(x-2)(-x^4color(black)(color(white)(00)-x^3-6x^2-21x)-7)/color(black)(")"bar(-x^4-4x^3-9x^2-7x-7)))# #color(white)((x-2)/(x-2)((color(black)(-x^4+2x^3)-9x^2-7x-7)/(color(black)bar(0x^4-6x^3-9x^2)-7x-7)))# #color(white)((x-2)/(x-2)((color(black)(color(white)(-x^4)-6x^3+12x^2)-7x-7)/(color(black)bar(color(white)(0x^4-)0x^3-21x^2-7x)-7)))# #color(white)((x-2)/(x-2)((color(black)(color(white)(-x^4-2x^3)-21x^2+42x)-7)/(color(black)bar(color(white)(0x^4-0x^3)-0x^2-49x-7))))#
We multiply #x# by #-49# to get to #-49x# and so we have:
#color(white)((x-2)/color(black)(x-2)(-x^4color(black)(color(white)(00)-x^3-6x^2-21x-49))/color(black)(")"bar(-x^4-4x^3-9x^2-7x-7)))# #color(white)((x-2)/(x-2)((color(black)(-x^4+2x^3)-9x^2-7x-7)/(color(black)bar(0x^4-6x^3-9x^2)-7x-7)))# #color(white)((x-2)/(x-2)((color(black)(color(white)(-x^4)-6x^3+12x^2)-7x-7)/(color(black)bar(color(white)(0x^4-)0x^3-21x^2-7x)-7)))# #color(white)((x-2)/(x-2)((color(black)(color(white)(-x^4-2x^3)-21x^2+42x)-7)/(color(black)bar(color(white)(0x^4-0x^3)-0x^2-49x-7))))# #color(white)((x-2)/(x-2)((color(black)(color(white)(-x^4-2x^3-1x^2)-49x+98))/(color(black)bar(color(white)(0x^4-0x^3-0x^2)-0x-105))))#
And so #(-x^4-4^3-9x^2-7x-7)/(x-2)=-x^3-6x^2-21x-49# with a remainder of #-105#
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Answer 2

To divide (-x^4-4x^3-9x^2-7x-7) by (x-2), you can use long division. Here are the steps:

  1. Start by dividing the first term of the numerator (-x^4) by the first term of the denominator (x). This gives you -x^3.

  2. Multiply the entire denominator (x-2) by -x^3, which gives you -x^4 + 2x^3.

  3. Subtract this result from the original numerator (-x^4-4x^3-9x^2-7x-7). This gives you -6x^3-9x^2-7x-7.

  4. Bring down the next term (-6x^3) and repeat the process. Divide (-6x^3) by (x), which gives you -6x^2.

  5. Multiply the entire denominator (x-2) by -6x^2, which gives you -6x^3 + 12x^2.

  6. Subtract this result from the previous step (-6x^3-9x^2-7x-7). This gives you 3x^2-7x-7.

  7. Bring down the next term (3x^2) and repeat the process. Divide (3x^2) by (x), which gives you 3x.

  8. Multiply the entire denominator (x-2) by 3x, which gives you 3x^2 - 6x.

  9. Subtract this result from the previous step (3x^2-7x-7). This gives you x-7.

  10. Bring down the next term (x) and repeat the process. Divide (x) by (x), which gives you 1.

  11. Multiply the entire denominator (x-2) by 1, which gives you x-2.

  12. Subtract this result from the previous step (x-7). This gives you 5.

The final result of the division is -x^3 - 6x^2 + 3x + 1 with a remainder of 5.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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