Given $f (x) = x + 2, g (x) = x - 3, h (x) = x + 4$ $f(x)=x+2, g(x)=x-3, h(x)=x+4$ how do you determine $y = f (x) g (x) h (x)$ $y=f(x)g(x)h(x)$ ?

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Answer 1 · 2017-02-18T03:23:19

$x^{3} + 3 x^{2} - 10 x - 24$ $x^3 +3x^2 - 10x -24$

Use substitution:
$y = f (x) \cdot g (x) \cdot h (x) = (x + 2) (x - 3) (x + 4)$ $y = f(x)*g(x)*h(x) = (x+2)(x-3)(x+4)$

Distribute the first two factors: $(x^{2} + 2 x - 3 x - 6) (x + 4)$ $(x^2+2x-3x-6)(x+4)$

Simplify: $(x^{2} - x - 6) (x + 4)$ $(x^2-x-6)(x+4)$

Distribute and add like-terms:
$x^{3} + 4 x^{2} - x^{2} - 4 x - 6 x - 24$ $x^3 + 4x^2 -x^2 -4x -6x -24$

$= x^{3} + 3 x^{2} - 10 x - 24$ $= x^3 +3x^2 - 10x -24$

Given f(x)=x+2, g(x)=x-3, h(x)=x+4f(x)=x+2,g(x)=x−3,h(x)=x+4f(x)=x+2, g(x)=x-3, h(x)=x+4 how do you determine y=f(x)g(x)h(x)y=f(x)g(x)h(x)y=f(x)g(x)h(x)?