Explanation:
Given that
[tex]p(x)=3x+5,q(x)=4x-5[/tex]
Part A:
Find
[tex]p(x)-q(x)[/tex]
By substituting the values, we will have
[tex]\begin{gathered} p(x)-q(x)=3x+5-(4x-5) \\ p(x)-q(x)=3x+5-4x+5 \\ p(x)-q(x)=3x-4x+5+5 \\ p(x)-q(x)=-x+10 \\ p(x)-q(x)=10-x \end{gathered}[/tex]
Hence,
The final answer is
[tex]p(x)-q(x)=10-x[/tex]
Part B:
Find,
[tex]p(x)+q(x)[/tex]
By substituting the values, we will have
[tex]\begin{gathered} p(x)+q(x) \\ p(x)+q(x)=3x+5+4x-5 \\ p(x)+q(x)=3x+4x+5-5 \\ p(x)+q(x)=7x \end{gathered}[/tex]
Hence,
The final answer is
[tex]p(x)+q(x)=7x[/tex]
Part C:
Find,
[tex]p(x)q(x)[/tex]
By substituting the values, we will have
[tex]\begin{gathered} p(x)q(x)=(3x+5)(4x-5) \\ p(x)q(x)=3x(4x-5)+5(4x-5) \\ p(x)q(x)=12x^2-15x+20x-25 \\ p(x)q(x)=12x^2+5x-25 \end{gathered}[/tex]
Hence,
The final answer is
[tex]p(x)q(x)=12x^{2}+5x-25[/tex]
