f(x) = x⁵ + 3x⁴ − x³ − 3x² + 5x + 15, g(x) = x + 3

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Solution

It is given that and

By the factor theorem, g(x) is the factor of polynomial f(x).

i.e.

f (−3) = 0

Hence, g(x) is the factor of polynomial f (x).

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Similar questions

Use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x)

f(x) = $x^{5} + 3 x^{4} - x^{3} - 3 x^{2}$ + 5x + 15, g(x) = x + 3

lim x \to - 2 \frac{x^{4} + 2 x^{3} + 3 x^{2} + 5 x - 2}{x^{5} + 3 x^{4} + 2 x^{3} + 3 x^{2} + 7 x + 2}

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

x^{2}

f (x) = \sqrt{x}

g (x) = \frac{3 x^{2} - x^{6}}{1 - 3 x^{4}}

h (x) = tan x,

(g \circ f \circ h) (\frac{π}{3})

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

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