How do you divide #(4x^4 -5x^2-2x+24)/((x + 4) )#?

Question

How do you divide #(4x^4 -5x^2-2x+24)/((x  + 4) )#?

Ethan Adkins · Accepted Answer

#4x^3-16x^2+59x-238+976/(x+4)# #"one way is to use the divisor as a factor in the numerator"# #"consider the numerator"# #color(red)(4x^3)(x+4)color(magenta)(-16x^3)-5x^2-2x+24# #=color(red)(4x^3)(x+4)color(red)(-16x^2)(x+4)color(magenta)(+64x^2)-5x^2-2x+24# #=color(red)(4x^3)(x+4)color(red)(-16x^2)(x+4)color(red)(+59x)(x+4)color(magenta)(-236x)-2x+24# #=color(red)(4x^3)(x+4)color(red)(-16x^2)(x+4)color(red)(+59x)(x+4)color(red)# #color(white)(=)color(red)(-238)(x+4)color(magenta)(+952)+24# #"quotient "=color(red)(4x^3-16x^2+59x-238)# #"remainder "=976# #rArr(4x^4-5x^2-2x+24)/(x+4)# #=4x^3-16x^2+59x-238+976/(x+4)#

Jameson Allen · Answer

undefined To divide (4x^4 - 5x^2 - 2x + 24) by (x + 4), you can use long division. Here are the steps:

1. Divide the first term of the dividend (4x^4) by the first term of the divisor (x). This gives you 4x^3.
2. Multiply the entire divisor (x + 4) by the quotient obtained in step 1 (4x^3). This gives you 4x^4 + 16x^3.
3. Subtract the result obtained in step 2 from the original dividend (4x^4 - 5x^2 - 2x + 24) to get the new dividend: -16x^3 - 5x^2 - 2x + 24.
4. Repeat steps 1-3 with the new dividend (-16x^3 - 5x^2 - 2x + 24) until you have no more terms to divide.
5. The final quotient is the sum of all the quotients obtained in each step, and any remaining terms form the remainder.

Therefore, the division of (4x^4 - 5x^2 - 2x + 24) by (x + 4) is 4x^3 - 16x^2 + 62x - 248 with a remainder of 1000.