How do you find the quotient of #(2h^3+8h^2-3h-12)div(h+4)#?

Question

Eva Abramson · Accepted Answer

#2h^2-3#

I'm going to rewrite this as:

#(2h^3+8h^2-3h-12)/(h+4)#

We can factor the numerator this way:

#((2h^3+8h^2)+(-3h-12))/(h+4)#

#(2h^2(h+4)+(-3)(h+4))/(h+4)#

#((2h^2-3)(h+4))/(h+4)#

We can now cancel the #(h+4)# on top and bottom:

#((2h^2-3)cancel((h+4)))/cancel((h+4))#

And be left with:

#2h^2-3#

Nathan Axel · Answer

undefined To find the quotient of (2h^3+8h^2-3h-12) divided by (h+4), you can use long division. Here are the steps:

1. Divide the first term of the dividend (2h^3) by the first term of the divisor (h). The result is 2h^2.
2. Multiply the divisor (h+4) by the quotient obtained in step 1 (2h^2). The result is 2h^3+8h^2.
3. Subtract the product obtained in step 2 from the dividend (2h^3+8h^2-3h-12) to get the new dividend: -11h^2-3h-12.
4. Repeat steps 1-3 with the new dividend (-11h^2-3h-12).
   - Divide the first term of the new dividend (-11h^2) by the first term of the divisor (h). The result is -11h.
   - Multiply the divisor (h+4) by the quotient obtained in this step (-11h). The result is -11h^2-44h.
   - Subtract the product obtained in this step from the new dividend (-11h^2-3h-12) to get the new dividend: 41h-12.
5. Repeat steps 1-3 with the new dividend (41h-12).
   - Divide the first term of the new dividend (41h) by the first term of the divisor (h). The result is 41.
   - Multiply the divisor (h+4) by the quotient obtained in this step (41). The result is 41h+164.
   - Subtract the product obtained in this step from the new dividend (41h-12) to get the remainder: -176.

Therefore, the quotient of (2h^3+8h^2-3h-12) divided by (h+4) is 2h^2-11h+41 with a remainder of -176.