How do you divide #(-7x^3-15x^2-24x-4)/(x-4) #?

Question

How do you divide #(-7x^3-15x^2-24x-4)/(x-4)  #?

Abigail Allen · Accepted Answer

#-7x^2-43x-196-788/(x-4)# #"one way is to use the divisor as a factor in the numerator"# #"consider the numerator"# #color(red)(-7x^2)(x-4)color(magenta)(-28x^2)-15x^2-24x-4# #=color(red)(-7x^2)(x-4)color(red)(-43x)(x-4)color(magenta)(-172x)-24x-4# #=color(red)(-7x^2)(x-4)color(red)(-43x)(x-4)color(red)(-196)(x-4)color(magenta)(-784)-4# #=color(red)(-7x^2)(x-4)color(red)(-43x)(x-4)color(red)(-196)(x-4)-788# #"quotient "=color(red)(-7x^2-43x-196)," remainder "=-788# #rArr(-7x^3-15x^2-24x-4)/(x-4)# #=-7x^2-43x-196-788/(x-4)#

Ethan Adkins · Answer

undefined To divide (-7x^3-15x^2-24x-4) by (x-4), you can use long division. Here are the steps:

1. Divide the first term of the numerator (-7x^3) by the first term of the denominator (x). The result is -7x^2.
2. Multiply the entire denominator (x-4) by -7x^2, giving -7x^3 + 28x^2.
3. Subtract this result (-7x^3 + 28x^2) from the numerator (-7x^3-15x^2-24x-4). This gives -43x^2 - 24x - 4.
4. Bring down the next term from the numerator, which is -43x^2. Now you have -43x^2 - 24x - 4.
5. Divide the first term of this new numerator (-43x^2) by the first term of the denominator (x). The result is -43x.
6. Multiply the entire denominator (x-4) by -43x, giving -43x^2 + 172x.
7. Subtract this result (-43x^2 + 172x) from the numerator (-43x^2 - 24x - 4). This gives -196x - 4.
8. Bring down the next term from the numerator, which is -196x. Now you have -196x - 4.
9. Divide the first term of this new numerator (-196x) by the first term of the denominator (x). The result is -196.
10. Multiply the entire denominator (x-4) by -196, giving -196x + 784.
11. Subtract this result (-196x + 784) from the numerator (-196x - 4). This gives -788.
12. There are no more terms left in the numerator, so the division is complete.

The quotient is -7x^2 - 43x - 196, and the remainder is -788.