22
Answer: 2a-6+--------------
a+4
Step-by-step explanation:
with the long-division set-up:
long-division set-up
Looking only at the leading terms, I divide 3x3 by 3x to get x2. This is what I put on top:
x^2 up on top
I multiply this x2 by the 3x + 1 to get 3x3 + 1x2, which I put underneath:
3x^3 + 3x put down underneath the dividend
Then I change the signs, add down, and remember to carry down the "+10x – 3" from the original dividend, giving me a new bottom line of –6x2 + 10x – 3:
(3x^3 – 5x^2 + 10x – 3) – (3x^3 + 1x^2) = –6x^2 + 10x – 3
Dividing the new leading term, –6x2, by the divisor's leading term, 3x, I get –2x, so I put this on top:
(–6x^2) ÷ (3x) = –2x, which goes on top
Then I multiply –2x by 3x + 1 to get –6x2 – 2x, which I put underneath. I change signs, add down, and remember to carry down the "–3 from the dividend:
(–6x^2 + 10x –3) – (–6x^2 – 2x) = 12x – 3, which is my new last line
My new last line is "12x – 3. Dividing the new leading term of 12x by the divisor's leading term of 3x, I get +4, which I put on top. I multiply 4 by 3x + 1 to get 12x + 4. I switch signs and add down. I end up with a remainder of –