Question

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

A) x3 + 3x2 + 16x − 20
B) x3 + 5x2 + 14x − 20
C) x3 + 8x2 + 11x − 20
D) x3 + 9x2 + 19x − 20

Answer 1

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

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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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Answer 2

`x^3 + 8x^2 + 11x-20`

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`