How do you divide #(3x^3 - 12x^2 - 11x - 20)/(x+5)#?

Question

Hazel Anglin · Accepted Answer

#(3x^3−12x^2−11x−20)/(x+5)=3x^2-27x+124-640/(x+5)# #(3x^3−12x^2−11x−20)-:(x+5)=3x^2-27x+124# #(3x^3+15x^2)/# #color(white)(..)0-27x^2-11x-20# #color(white)(....)(-27x^2-135x)/# #color(white)(...........)0+124x-20# #color(white)(..............)(+124x+620)/# #color(white)(......................)0-640# #(3x^3−12x^2−11x−20)/(x+5)=3x^2-27x+124+(-640)/(x+5)#

Genesis Allen · Answer

#3x^2-27x+124-640/(x+5)# #"one way is to use the divisor as a factor in the numerator"# #"consider the numerator"# #color(red)(3x^2)(x+5)color(magenta)(-15x^2)-12x^2-11x-20# #=color(red)(3x^2)(x+5)color(red)(-27x)(x+5)color(magenta)(+135x)-11x-20# #=color(red)(3x^2)(x+5)color(red)(-27x)(x+5)color(red)(+124)(x+5)color(magenta)(-620)-20# #=color(red)(3x^2)(x+5)color(red)(-27x)(x+5)color(red)(+124)(x+5)-640# #"quotient "=color(red)(3x^2-27x+124)," remainder "=-640# #rArr(3x^3-12x^2-11x-20)/(x+5)# #=3x^2-27x+124-640/(x+5)#

Eva Abramson · Answer

undefined To divide (3x^3 - 12x^2 - 11x - 20) by (x+5), you can use long division. Here are the steps:

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+5) by the quotient obtained in step 1 (3x^2). This gives you 3x^3 + 15x^2.
3. Subtract the result obtained in step 2 from the dividend (3x^3 - 12x^2 - 11x - 20) to get a new polynomial: -27x^2 - 11x - 20.
4. Repeat steps 1-3 with the new polynomial (-27x^2 - 11x - 20).
   - Divide the first term of the new polynomial (-27x^2) by the first term of the divisor (x). This gives you -27x.
   - Multiply the divisor (x+5) by the quotient obtained (-27x). This gives you -27x^2 - 135x.
   - Subtract the result obtained from the new polynomial to get a new polynomial: 124x - 20.
5. Repeat steps 1-3 with the new polynomial (124x - 20).
   - Divide the first term of the new polynomial (124x) by the first term of the divisor (x). This gives you 124.
   - Multiply the divisor (x+5) by the quotient obtained (124). This gives you 124x + 620.
   - Subtract the result obtained from the new polynomial to get a remainder of -640.

Therefore, the quotient is 3x^2 - 27x + 124 with a remainder of -640.