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Given that f(x) = x2 + 10x + 21 and g(x) = x + 3, find f(x) · g(x) and express the result in standard form.

Sagot :

absor201

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]

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