Property 10
| \(P(x)\) | \(x-a\) |
| _ | \(B(x)\) |
| \(K\) |
If a polynomial is divided by a linear polynomial; the remainder is a constant number.
\(P(x)=(x-a)\cdot B(x)+K\)
\(x=a \Rightarrow P(a)=K\)
1.
| \(x^3-2x+1\) | \(x+1\) |
| _ |
| \(K(x)\) |
\(\Rightarrow K(x)=?\)
2.
| \(x^4-3x+1\) | \(x-2\) |
| _ |
| \(K(x)\) |
\(\Rightarrow K(x)=?\)
3.
| \(P(x)\) | \(x-1\) |
| _ |
| \(K\) |
\(P(x-1)=x^2-3x+1\)
\(\Rightarrow K=?\)
4.
| \(P(x+1)\) | \(x-1\) |
| _ |
| \(K\) |
\(P(x-2)=x^3-2x+1\)
\(\Rightarrow K=?\)
5.
| \(P(x+1)\) | \(x+2\) |
| _ |
| \(K\) |
\(P(x-1)=x^2-ax+4\)
\(\Rightarrow K=?\)
6.
| \(P(x)\) | \(x-1\) |
| _ |
| \(2\) |
\(P(x)=x^2+ax-2\)
\(\Rightarrow a=?\)
7.
| \(P(x)\) | \(x-3\) |
| _ |
| \(6\) |
\(P(x)=ax^2+3x-2\)
\(\Rightarrow a=?\)
8.
| \(P(x-1)\) | \(x-2\) |
| _ |
| \(8\) |
\(P(x+1)=x^2-ax+6+b\)
\(\Rightarrow b=?\)
9.
| \(P(x)\) | \(x-1\) |
| _ |
| \(3\) |
| \(Q(x)\) | \(x+2\) |
| _ |
| \(2\) |
\(P(x+1)+2Q(x-2)=a(x-2)+4\)
\(\Rightarrow a=?\)
10.
| \(P(x)\) | \(x\) |
| _ |
| \(4\) |
| \(Q(x)\) | \(x+1\) |
| _ |
| \(2\) |
\(P(x+2)+Q(x+1)=x^2-2ax-4\)
\(\Rightarrow a=?\)
11.
| \(P(x+1)\) | \(x-1\) |
| _ |
| \(2\) |
| \(Q(x)\) | \(x-2\) |
| _ |
| \(3\) |
\(P(x)+Q(x)=2x+a\)
\(\Rightarrow a=?\)