How do you divide #( -3x^3+ 16x^2-24x+9 )/(x + 1 )#?

Answer 1

#-3x^3+16x^2-24x+9# is not divisible by #x+1#

If we descompose #-3x^3+16x^2-24x+9# we obtain: #(x-3)(-3x^2+7x+3)# which is not divisible by #x+1#.
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Answer 2

#-3x^2+19x-43+52/(x+1)#

#"one way is to use the divisor as a factor in the numerator"#
#"consider the numerator"#
#color(red)(-3x^2)(x+1)color(magenta)(+3x^2)+16x^2-24x+9#
#=color(red)(-3x^2)(x+1)color(red)(+19x)(x+1)color(magenta)(-19x)-24x+9#
#=color(red)(-3x^2)(x+1)color(red)(+19x)(x+1)color(red)(-43)(x+1)color(magenta)(+43)+9#
#=color(red)(-3x^2)(x+1)color(red)(+19x)(x+1)color(red)(-43)(x+1)+52#
#"quotient "=color(red)(-3x^2+19x-43)," remainder "=52#
#rArr(-3x^3+16x^2-24x+9)/(x+1)#
#=-3x^2+19x-43+52/(x+1)#
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Answer 3

To divide (-3x^3 + 16x^2 - 24x + 9) by (x + 1), you can use long division or synthetic division. Here is the step-by-step process using long division:

  1. Divide the first term of the dividend (-3x^3) by the first term of the divisor (x). This gives you -3x^2.
  2. Multiply the divisor (x + 1) by the quotient obtained in step 1 (-3x^2). This gives you -3x^3 - 3x^2.
  3. Subtract the result obtained in step 2 from the dividend (-3x^3 + 16x^2 - 24x + 9) to get the new dividend: (16x^2 - 24x + 9) - (-3x^3 - 3x^2) = 19x^2 - 24x + 9.
  4. Repeat steps 1-3 with the new dividend (19x^2 - 24x + 9).
  5. Divide the first term of the new dividend (19x^2) by the first term of the divisor (x). This gives you 19x.
  6. Multiply the divisor (x + 1) by the quotient obtained in step 5 (19x). This gives you 19x^2 + 19x.
  7. Subtract the result obtained in step 6 from the new dividend (19x^2 - 24x + 9) to get the new dividend: (-24x + 9) - (19x^2 + 19x) = -19x^2 - 43x + 9.
  8. Repeat steps 5-7 with the new dividend (-19x^2 - 43x + 9).
  9. Divide the first term of the new dividend (-19x^2) by the first term of the divisor (x). This gives you -19x.
  10. Multiply the divisor (x + 1) by the quotient obtained in step 9 (-19x). This gives you -19x^2 - 19x.
  11. Subtract the result obtained in step 10 from the new dividend (-19x^2 - 43x + 9) to get the remainder: (-43x + 9) - (-19x^2 - 19x) = -24x + 9.

Therefore, the quotient is -3x^2 + 19x - 19, and the remainder is -24x + 9.

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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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