Property 4
Addition and Subtraction of Polynomials
In addition and subtraction operations of polynomials equal degree terms are added or subtracted.
\(P(x)=2x^3-5x^2+7x+10\)
\(Q(x)=x^3+4x^2+5\)
\(P(x)+Q(x)=3x^3-x^2+7x+15\)
\(P(x)-Q(x)=x^3-9x^2+7x+5\)
Multiplication of Polynomials
In multiplication of polynomials the distribution over addition is used.
\(P(x)=x^2-x\)
\(Q(x)=2x-3\)
\(P(x)\cdot Q(x)=(x^2-x)\cdot(2x-3)\)
\(=2x^3-3x^2-2x^2+3x\)
\(=2x^3-5x^2+3x\)
1.
\(P(x)=2x^3+2x-1\)
\(Q(x)=x^2+6x+3\)
\(\Rightarrow P(x)+Q(x)=?\)
2.
\(P(x)=x^2-3x\)
\(Q(x)=2x^2+4\)
\(3P(x)-Q(x)=?\)
3.
\(P(x)=2x^2-3\)
\(Q(x)=x^3+x^2\)
\(\Rightarrow 2P(x)+3Q(x)=?\)
4.
\(P(x)=2x^2-3x\)
\(Q(x)=x^2\)
\(\Rightarrow Q(x)-2P(x)=?\)
5.
\(P(x)=x^3-x^4+x\)
\(Q(x)=-x^3-x^2+2\)
\(\Rightarrow P(x)-Q(x)=?\)
6.
\(P(x)=x^2\)
\(Q(x)=x-1\)
\(\Rightarrow P(x)\cdot Q(x)=?\)
7.
\(P(x)=x^2-1\)
\(Q(x)=x+1\)
\(\Rightarrow P(x)\cdot Q(x)=?\)
8.
\(P(x)=(x^3+x+1)\)
\(Q(x)=x+3\)
\(\Rightarrow P(x)\cdot Q(x)=?\)
9.
\(P(x)=3x^3-2x^2+5\)
\(Q(x)=2x-3\)
\(\Rightarrow P(x)\cdot Q(x)=?\)