Property 9
| \(P(x)\) | \(Q(x)\) |
| _ | \(B(x)\) |
| \(K(x)\) |
\(d[Q(x)]\leq d[P(x)]\)
\(P(x)\) : Divided
\(Q(x)\) : Divisor
\(B(x)\) : Division
\(K(x)\) : Remainder
- \(P(x)=Q(x)\cdot B(x)+K(x)\)
- \(d[K(x)]
1.
| \(x^5-2x^3+x^2-2\) | \(x^2-2\) |
| _ | \(B(x)\) |
| \(K(x)\) |
\(\Rightarrow B(x)=?\)
2.
| \(x^4+x^3+2x^2+x+1\) | \(x^2+1\) |
| _ | \(B(x)\) |
| \(K(x)\) |
\(\Rightarrow B(x)=?\)
3.
| \(x^4+x^3-x^2-2x\) | \(x+1\) |
| _ | \(B(x)\) |
| \(K(x)\) |
\(\Rightarrow B(x)=?\)
4.
| \(x^5+x^3-x^2-x\) | \(x^3-1\) |
| _ | \(B(x)\) |
| \(K(x)\) |
\(\Rightarrow B(x)=?\)
5.
| \(2x^3+x^2+x\) | \(x^2-x-1\) |
| _ |
| \(K(x)\) |
\(\Rightarrow K(x)=?\)
6.
| \(x^3-5x^2+4x+7\) | \(x^2-3\) |
| _ |
| \(K(x)\) |
\(\Rightarrow K(x)=?\)
7.
| \(2x^4-3x^2+x\) | \(x^2+x\) |
| _ | \(B(x)\) |
| \(K(x)\) |
\(\Rightarrow K(x)=?\)
8.
| \(x^3+x^2+x\) | \(x^2-x-1\) |
| _ | \(B(x)\) |
| \(K(x)\) |
\(\Rightarrow K(x)=?\)
9.
| \(x^3-4x^2+mx+n\) | \(x^2-2x+5\) |
| _ | \(B(x)\) |
| \(0\) |
\(\Rightarrow m\cdot n=?\)