How do you divide #(7x^3+14x^2-3) /(x-3)#?

Question

Ethan Adkins · Accepted Answer

Use either polynomial long division or synthetic division to get:
#(7x^2+35x+105)# with a remainder of #(+312)# As polynomial long division, it looks like this: #{: (,,7x^2,+35x,+105,), (x-3,")",bar(7x^3),bar(+14x^2),bar(color(white)("XXX")),bar(-3)), (,,7x^3,-21x^2,,-3), (,,bar(color(white)("XXX")),bar(35x^2),bar(color(white)("XXX")),bar(-3)), (,,,35x^2,-105x,), (,,,bar(color(white)("XXX")),bar(105x),bar(-3)), (,,,,105x,-315), (,,,,bar(color(white)("XXX")),bar(+312)) :}#

Eli Assouline · Answer

undefined To divide (7x^3+14x^2-3) by (x-3), you can use long division. Here are the steps:

1. Divide the first term of the dividend (7x^3) by the first term of the divisor (x). This gives you 7x^2.
2. Multiply the entire divisor (x-3) by the quotient obtained in step 1 (7x^2). This gives you 7x^3 - 21x^2.
3. Subtract the result obtained in step 2 from the original dividend (7x^3+14x^2-3). This gives you 35x^2 - 3.
4. Bring down the next term from the dividend (-3) and append it to the result obtained in step 3. This gives you 35x^2 - 3.
5. Divide the first term of the new dividend (35x^2) by the first term of the divisor (x). This gives you 35x.
6. Multiply the entire divisor (x-3) by the quotient obtained in step 5 (35x). This gives you 35x^2 - 105x.
7. Subtract the result obtained in step 6 from the new dividend (35x^2 - 3). This gives you 102x.
8. Since there are no more terms in the dividend, the division is complete.

Therefore, the quotient is 7x^2 + 35x and the remainder is 102x.