How do you divide #( x^3-4x^2-17x+60 )/(3-2x)#?

Answer 1

#-1/2x^2+5/4x+83/8 +231/(8(3-2x))" Corrected"#

#color(white)("-----------------------------")+x^3-4x^2-17x+60# #color(magenta)(-1/2x^2)(3-2x)->color(white)("-----")ul(+x^3-3/2x^2 larr" Subtract ") # #color(white)("--------------------------------")0color(white)("-")-5/2x^2-17x+60 color(red)(larr" Corrected"# #color(magenta)(+5/4x)(3-2x)->color(white)("------------") ul(-5/2x^2+15/4x larr" Subtract")# #color(white)("---------------------------------------")0 color(white)("----")-83/4x+60#
#color(magenta)(+83/8)(3-2x)->color(white)("----------------------")ul(-83/4x+249/8larr" Subt.")# #color(magenta)("Remainder"->color(white)("--------------------------------") 0+231/8)#

Giving:

#color(magenta)( -1/2x^2+5/4x+83/8 +231/(8(3-2x)))#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

#-1/2x^2+5/4x+83/8+(231)/(8(-2x+3))#

#(x^3-4x^2-17x+60)/(3-2x)#
#color(white)(..........)color(white)(...)-1/2x^2+5/4x+83/8# #-2x+3|overline(x^3-4x^2-17x+60)# #color(white)(................)ul(x^3-3/2x^2)# #color(white)(......................)-5/2x^2-17x# #color(white)(......................)ul(-5/2x^2+15/4x)# #color(white)(.................................)-83/4x+60# #color(white)(..................................)ul(-83/4x+249/8)# #color(white)(................................................)231/8#
#(x^3-4x^2-17x+60)/(3-2x) = -1/2x^2+5/4x+83/8+(231)/(8(-2x+3))#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 3

To divide (x^3-4x^2-17x+60) by (3-2x), you can use polynomial long division. Here are the steps:

  1. Arrange the dividend (x^3-4x^2-17x+60) and the divisor (3-2x) in descending order of powers of x.

  2. Divide the first term of the dividend (x^3) by the first term of the divisor (3) to get x^2.

  3. Multiply the divisor (3-2x) by the quotient obtained in step 2 (x^2), and subtract the result from the dividend.

  4. Bring down the next term of the dividend (-4x^2) and repeat steps 2 and 3.

  5. Continue this process until all terms of the dividend have been divided.

  6. The final result will be the quotient (x^2+2x-5) and the remainder (-5x+75).

Therefore, (x^3-4x^2-17x+60)/(3-2x) = x^2+2x-5 with a remainder of -5x+75.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7