Question

Divide
x-4) 2x^3 + 4x^2 +6x +9(​

Answer 1

Divide 3x3 – 5x2 + 10x – 3 by 3x + 1

I start 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

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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 –7:

(12x)/(3x) = 4, 4(3x + 1) = 12x + 4, (12x – 3) – (12x + 4) = –7