Question

Let f(x) = x2 + 3x − 4 and g(x) = x + 5. Find f(x) ⋅ g(x).

Answer 1

Answer:

 $x^3 + 8x^2 + 11x-20$

Step-by-step explanation:

f(x) = x^2 + 3x − 4

g(x) = x + 5

To find f(x) * g(x) we multiply f(x) with g(x)

$f(x) * g(x) = (x^2 + 3x -4) * (x+5)$

First multiply each term in f(x) and multiply with x+5

x^2 times x+5 becomes $x^3+5x^2$

3x times x+5 becomes $3x^2 + 15x$

-4 times x+ 5 becomes -4x -20

so f(x) * g(x) = $x^3 + 5x^2 +3x^2 + 15x -4x -20$

Combine like terms

f(x) * g(x) = $x^3 + 8x^2 + 11x-20$

Answer 2

Answer:    [C]:    " x³ + 8x² + 11x − 20 " .

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Step-by-step explanation:

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Given:      "  f(x) =  x² + 3x − 4 " ;   and

                " g(x) =  x + 5  "  ;

Find:         "  f(x) ⋅ g(x) "  :

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    f(x) ⋅ g(x) =

     " (x² + 3x − 4) (x + 5) " ;

     ↔  " (x + 5) (x² + 3x − 4) " ;

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Note:  " (a + b) (c + d + e)  =  ac + ad + ae + bc + bd + ae " ;

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 →  " (x + 5) (x² + 3x − 4)

             =  (x * x²) + (x * 3x) + (x*-4) + (5*x²) + (5*3x) + (5*-4) " ;

             =  (x³) + (3x²)  + (-4x) + (5x²) + (15x) + (-20) ;

             =   x³  + 3x² − 4x + 5x² + 15x − 20 ;

 →  Combine the "like terms" :

          + 3x² + 5x²  =  + 8x²  ;

           − 4x + 15x   = + 11 x ;

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 → And rewrite:

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        →   "  x³ +  8x²  +  11x  − 20 " ;

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       →  which is:  Answer choice:  [C]:   " x³  +  8x²  +  11x  −  20 " .

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     Hope this helps!

        Best wishes!

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