How do you long divide 6x3+3x2−4x+7 by x2+1?

1 Answer
Alberto M.
Jun 15, 2015

6x+3+−10x+4x2+1

Explanation:

Let's write
A(x)=6x3+3x2−4x+7 and
B(x)=x2+1

We use the rule: we find the first term dividing the term with the highest degree in A(x) by the term with the highest degree in B(x), let's call it q3−2x3−2 then we calculate P1(x)=A(x)−B(x)⋅Q3−2(x), which has degree 2

6x3x2=6x⇒P1(x)=6x3+3x2−4x+7−6x(x2+1)=3x2−10x+7

Now we consider the same process with P1(x), and we have q3−2−1x3−2−1 and R(x).

3x2x2=3⇒R(x)=3x2−10x+7−3(x2+1)=−10x+4

Notice that

∂(R(x))<∂(B(x))

so we're done, and Q(x)=q3−2x3−2+q3−2−1x3−2−1=6x+3 is the quotient and R(x) is the reminder

NB: I consider ∂(P) as the degree of P

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