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The question is asking for the quotient and remainder of
(2x^4 - 6x^3 + x - 1)/(x+2)
The first term of the quotient will be 2x^3. This reduces the problem to
= 2x^3 + (-10x^3 + x -1)/(x+2)
The second term of the quotient will be -10x^2. This reduces the problem to
= 2x^3 - 10x^2 + (20x^2 + x - 1)/(x+2)
The third term of the quotient will be 20x. This reduces the problem to
= 2x^3 - 10x^2 + 20x + (-39x - 1)/(x+2)
The last term of the quotient will be -39. The answer thus becomes
F(x) = (x+2)(2x^3 - 10x^2 + 20x - 39) + 77
(2x^4 - 6x^3 + x - 1)/(x+2)
The first term of the quotient will be 2x^3. This reduces the problem to
= 2x^3 + (-10x^3 + x -1)/(x+2)
The second term of the quotient will be -10x^2. This reduces the problem to
= 2x^3 - 10x^2 + (20x^2 + x - 1)/(x+2)
The third term of the quotient will be 20x. This reduces the problem to
= 2x^3 - 10x^2 + 20x + (-39x - 1)/(x+2)
The last term of the quotient will be -39. The answer thus becomes
F(x) = (x+2)(2x^3 - 10x^2 + 20x - 39) + 77
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Thank you so much! But how did you get each quotient?
Divide the highest power term of the dividend by the highest power term of the divisor. These are, in order, 2x^4/x=2x^3, -10x^3/x=-10x^2, 20x^2/x=20x, -39x/x=-39.
Just as in all-numeric long division, the dividend for the next level results from subtracting quotient*divisor from dividend at this level. To get the second level, you are subtracting 2x^3(x+2)=2x^4+4x^3 from the original expression. To get the third level you are subtracting -10x^2(x+2)=-10x^3-20x^2 from that.
Just as in all-numeric long division, the dividend for the next level results from subtracting quotient*divisor from dividend at this level. To get the second level, you are subtracting 2x^3(x+2)=2x^4+4x^3 from the original expression. To get the third level you are subtracting -10x^2(x+2)=-10x^3-20x^2 from that.
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