If f(x) = $2 x^{2} - 5 x + 1$ and g(x) = $- x^{3} - x^{2} - 3 x + 2$ , find g(x) - f(x).

- x^{3} - x^{2} + 2 x + 1

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- 2 x^{3} - 5 x^{2} + 5 x + 1

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- 2 x^{3} - 3 x^{2} + 2 x - 4

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- x^{3} - 3 x^{2} + 2 x + 1

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Solution

The correct option is D $- x^{3} - 3 x^{2} + 2 x + 1$
Given: f(x) = $2 x^{2} - 5 x + 1$ and g(x) = $- x^{3} - x^{2} - 3 x + 2$

$g (x) - f (x) = (- x^{3} - x^{2} - 3 x + 2) - (2 x^{2} - 5 x + 1)$
$g (x) - f (x) = - x^{3} - x^{2} - 2 x^{2} - 3 x + 5 x + 2 - 1$
$g (x) - f (x) = - x^{3} - 3 x^{2} + 2 x + 1$

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f (x) = 2 x^{4} - 5 x^{3} + x^{2} + 3 x - 2

q (x) = 2 x^{2} - 5 x + 3 a n d r (x) = - 2 x + 1

f (x) = 2 x^{4} - 5 x^{3} + x^{2} + 3 x - 2

g (x)

q (x) = 2 x^{2} - 5 x + 3

r (x) = - 2 x + 1

g (x)

g (x) = x^{2} + x - 2

\frac{1}{2} (g \circ f) (x) = 2 x^{2} - 5 x + 2

f (x)

Divide $f (x)$ by $g (x)$ and find the quotient.
$f (x) = x^{3} - 125, g (x) = x^{2} + 5 x + 25$

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