Question

The quotient of (x^4+5x^3-3x-15) and a polynomial is (x^3-3). What is the polynomial?

Answer 1

Let f(x) be the required polynomial.

Then, $\frac{x^{4}+5x^{3}-3x-15}{f(x)} =x^{3} -3$

Or, $f(x) = \frac{x^{4}+15x^{3}-3x-15}{x^{3}-3 }$

Consider the numerator.

$x^{4} +5x^{3} -3x-15 = x^{3}(x + 5)-3(x + 5)$

$=(x^{3}- 3)(x+5)$

Therefore, $\frac{x^{4}+5x^{3}-3x-15}{x^{3}-3 }$

= $\frac{(x^{3}-3)(x+5) }{x^{3}-3 }$

= x + 5

Answer 2

Answer:

x+5

Step-by-step explanation:

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