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Answer:
We conclude that:
[tex]f\left(x\right)\cdot g\left(x\right)=x^3+13x^2+51x+63[/tex]
Step-by-step explanation:
Given
[tex]f\left(x\right)=\left(\:x^2\:+\:10x\:+\:21\right)[/tex]
[tex]g(x)=x+3[/tex]
Determining f(x) · g(x)
[tex]f\left(x\right)\cdot g\left(x\right)=\left(\:x^2\:+\:10x\:+\:21\right)\times \left(x+3\right)[/tex]
Distribute parentheses
[tex]=x^2x+x^2\times \:3+10xx+10x\times \:3+21x+21\times \:3[/tex]
[tex]=x^2x+3x^2+10xx+10\times \:3x+21x+21\times \:3[/tex]
[tex]=x^3+3x^2+10x^2+30x+21x+63[/tex]
Add similar elements: [tex]3x^2+10x^2=13x^2[/tex]
[tex]=x^3+13x^2+30x+21x+63[/tex]
Add similar elements: [tex]30x+21x=51x[/tex]
[tex]=x^3+13x^2+51x+63[/tex]
Therefore, we conclude that:
[tex]f\left(x\right)\cdot g\left(x\right)=x^3+13x^2+51x+63[/tex]