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Let \(f(x)=x+5\) and let \(g(x)=x^2+1\). Let  \(p(x)=g(x)+f(x)\)and let \(q(x)=g(x)-f(x)\). Find \(p(x)\cdot q(x)\).

 

Help please!

mathtoo  Aug 1, 2018

Best Answer 

 #1
avatar+20680 
+2

Let
\(f(x)=x+5\)
and let
\(g(x)=x^2+1\).
Let
\(p(x)=g(x)+f(x)\)
and let
\(q(x)=g(x)-f(x)\).
Find
\(p(x)\cdot q(x)\).

 

\(\begin{array}{|rcll|} \hline p(x)\cdot q(x) &=& \Big( g(x)+f(x) \Big) \Big( g(x)-f(x) \Big) \\ &=& [g(x)]^2-[f(x)]^2 \\ &=& (x^2+1)^2-(x+5)^2 \\ &=& x^4+2x^2+1 -(x^2+10x+25) \\ &=& x^4+2x^2+1 -x^2-10x-25 \\ &\mathbf{=}& \mathbf{x^4+x^2-10x-24} \\ \hline \end{array}\)

 

laugh

heureka  Aug 1, 2018
 #1
avatar+20680 
+2
Best Answer

Let
\(f(x)=x+5\)
and let
\(g(x)=x^2+1\).
Let
\(p(x)=g(x)+f(x)\)
and let
\(q(x)=g(x)-f(x)\).
Find
\(p(x)\cdot q(x)\).

 

\(\begin{array}{|rcll|} \hline p(x)\cdot q(x) &=& \Big( g(x)+f(x) \Big) \Big( g(x)-f(x) \Big) \\ &=& [g(x)]^2-[f(x)]^2 \\ &=& (x^2+1)^2-(x+5)^2 \\ &=& x^4+2x^2+1 -(x^2+10x+25) \\ &=& x^4+2x^2+1 -x^2-10x-25 \\ &\mathbf{=}& \mathbf{x^4+x^2-10x-24} \\ \hline \end{array}\)

 

laugh

heureka  Aug 1, 2018

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