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

Answer 1

#x^2-7x+15-20/(x+2)#

#"one way is to use the divisor as a factor in the numerator"#
#"consider the rearranged numerator"#
#x^3-5x^2+x+10#
#=color(red)(x^2)(x+2)color(magenta)(-2x^2)-5x^2+x+10#
#=color(red)(x^2)(x+2)color(red)(-7x)(x+2)color(magenta)(+14x)+x+10#
#=color(red)(x^2)(x+2)color(red)(-7x)(x+2)color(red)(+15)(x+2)color(magenta)(-30)+10#
#=color(red)(x^2)(x+2)color(red)(-7x)(x+2)color(red)(+15)(x+2)-20#
#"quotient "=color(red)(x^2-7x+15)," remainder "=-20#
#(x-5x^2+10+x^3)/(x+2)=x^2-7x+15-20/(x+2)#
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Answer 2

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

  1. Divide the first term of the numerator (x^3) by the first term of the denominator (x). This gives x^2.
  2. Multiply the entire denominator (x+2) by the quotient obtained in step 1 (x^2). This gives x^3+2x^2.
  3. Subtract the result obtained in step 2 from the numerator (x-5x^2+10+x^3). This gives -7x^2+10.
  4. Bring down the next term from the numerator (-7x^2+10), which is -7x^2.
  5. Divide the first term of the new numerator (-7x^2) by the first term of the denominator (x). This gives -7x.
  6. Multiply the entire denominator (x+2) by the quotient obtained in step 5 (-7x). This gives -7x^2-14x.
  7. Subtract the result obtained in step 6 from the new numerator (-7x^2+10). This gives 24x+10.
  8. Bring down the next term from the numerator (24x+10), which is 24x.
  9. Divide the first term of the new numerator (24x) by the first term of the denominator (x). This gives 24.
  10. Multiply the entire denominator (x+2) by the quotient obtained in step 9 (24). This gives 24x+48.
  11. Subtract the result obtained in step 10 from the new numerator (24x+10). This gives -38.
  12. There are no more terms left in the numerator, so the division is complete.

The quotient is x^2 - 7x + 24, and the remainder is -38.

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Answer 3

To divide ( \frac{x - 5x^2 + 10 + x^3}{x + 2} ), you can use polynomial long division or synthetic division. Let's use polynomial long division.

  1. Divide the first term of the numerator by the first term of the denominator.
  2. Multiply the entire denominator by the quotient obtained in step 1.
  3. Subtract the result obtained in step 2 from the numerator.
  4. Repeat steps 1-3 until you obtain a remainder with degree less than the denominator.

Following these steps, the division yields a quotient of ( x^2 - 5x + 10 ) and a remainder of ( -20 ).

Therefore, ( \frac{x - 5x^2 + 10 + x^3}{x + 2} = x^2 - 5x + 10 - \frac{20}{x + 2} ).

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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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