How do you divide #(2x^3+7x^2-5x-4) / (2x+1)# using polynomial long division?

Answer 1

#x^2+3x-4 #

Numerator #->color(white)("d")2x^3+7x^2-5x-4# #color(magenta)(x^2)(2x+1)-> color(white)("d")ul(2x^3+x^2larr" Subtract"# #color(white)("dddddddddddddd") 0+6x^2-5x-4# #color(magenta)(3x)(2x+1)-> color(white)("dddddd") ul(6x^2+3xlarr" Subtract")# #color(white)("ddddddddddddddddddd")0-8x-4# #color(magenta)(-4)(2x+1) ->color(white)("ddddddd.d")ul(-8x-4 larr" Subtract")# #"Remainder"-> color(white)("ddddddddddd")0color(white)("d")+0#
#color(white)("dddddddddddddd")color(magenta)( x^2+3x-4 )#
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Answer 2

Quotient is #x^2+3x-4# and remainder is #0#

#2x^3+7x^2-5x-4#
=#2x^3+x^2+6x^2+3x-8x-4#
=#x^2*(2x+1)+3x*(2x+1)-4*(2x+1)#
=#(2x+1)*(x^2+3x-4)#
Hence quotient is #x^2+3x-4# and remainder is #0#
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Answer 3

To divide (2x^3+7x^2-5x-4) by (2x+1) using polynomial long division, follow these steps:

  1. Arrange the dividend (2x^3+7x^2-5x-4) and the divisor (2x+1) in descending order of exponents.
  2. Divide the first term of the dividend (2x^3) by the first term of the divisor (2x). The result is x^2.
  3. Multiply the divisor (2x+1) by the quotient obtained in step 2 (x^2). The result is 2x^3+x^2.
  4. Subtract the product obtained in step 3 (2x^3+x^2) from the dividend (2x^3+7x^2-5x-4). The result is 6x^2-5x-4.
  5. Bring down the next term from the dividend (-5x).
  6. Divide the first term of the new dividend (6x^2) by the first term of the divisor (2x). The result is 3x.
  7. Multiply the divisor (2x+1) by the quotient obtained in step 6 (3x). The result is 6x^2+3x.
  8. Subtract the product obtained in step 7 (6x^2+3x) from the new dividend (6x^2-5x-4). The result is -8x-4.
  9. Bring down the next term from the dividend (-4).
  10. Divide the first term of the new dividend (-8x) by the first term of the divisor (2x). The result is -4.
  11. Multiply the divisor (2x+1) by the quotient obtained in step 10 (-4). The result is -8x-4.
  12. Subtract the product obtained in step 11 (-8x-4) from the new dividend (-8x-4). The result is 0.

The quotient is x^2 + 3x - 4, and the remainder is 0.

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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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