How do you divide #x^3+6x^2-2x+3# by x-3?

Answer 1

#x^2+9x+25+78/(x-3)#

#" "x^3+6x^2-2x+3# #color(magenta)(x^2)(x-3) ->ul(x^3-3x^2larr" Subtract")# #" "0+9x^2-2x+3# #color(magenta)(9x)(x-3)->" "ul(9x^2-27xlarr" Subtract")# #" "0+25x+3# #color(magenta)(25)(x-3)->" "ul(25x-75larr" Subtract")# #" "color(magenta)(0+78 larr" Remainder")#
#color(magenta)( x^2+9x+25+78/(x-3))#
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Answer 2

To divide x^3+6x^2-2x+3 by x-3, you can use long division. The steps are as follows:

  1. Divide the first term of the dividend (x^3) by the divisor (x-3). The result is x^2.

  2. Multiply the divisor (x-3) by the result obtained in step 1 (x^2). The product is x^3-3x^2.

  3. Subtract the product obtained in step 2 from the original dividend (x^3+6x^2-2x+3). This gives you 9x^2-2x+3.

  4. Bring down the next term from the original dividend, which is -2x.

  5. Divide the term brought down (-2x) by the divisor (x-3). The result is -2.

  6. Multiply the divisor (x-3) by the result obtained in step 5 (-2). The product is -2x+6.

  7. Subtract the product obtained in step 6 from the remainder obtained in step 3 (9x^2-2x+3). This gives you 9x^2-4x-3.

  8. Bring down the next term from the original dividend, which is -3.

  9. Divide the term brought down (-3) by the divisor (x-3). The result is -1.

  10. Multiply the divisor (x-3) by the result obtained in step 9 (-1). The product is -x+3.

  11. Subtract the product obtained in step 10 from the remainder obtained in step 7 (9x^2-4x-3). This gives you 9x^2-3x-6.

The final result of the division is x^2-2x-1, with a remainder of 9x^2-3x-6.

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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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