Answer: Our required polynomial is given by
\(x+5\)
Step-by-step explanation:
Since we have given that
\(f(x)=x^4+5x^3-3x-15\)
And
\(q(x)=x^3-3\)
Since we know that
Euclid division lemma states that
\(f(x)=q(x)\times g(x)+r(x)\)
where,
\(f(x)\text{ denotes the dividend}\\g(x)\text{ denotes the required polynomial}\\q(x)\text{ denotes the quotient}\\r(x)\text{ denotes the remainder}\\\)
Now,
\(x^4+5x^3-3x-15=x^3-3\times g(x)+0\)
So, our equation becomes
\(g(x)\\\\=\frac{x^4+5x^3-3x-15}{x^3-3}\\\\=x+5\)
So, our required polynomial is given by
\(x+5\)
