Answer: Our required polynomial is given by
[tex]x+5[/tex]
Step-by-step explanation:
Since we have given that
[tex]f(x)=x^4+5x^3-3x-15[/tex]
And
[tex]q(x)=x^3-3[/tex]
Since we know that
Euclid division lemma states that
[tex]f(x)=q(x)\times g(x)+r(x)[/tex]
where,
[tex]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}\\[/tex]
Now,
[tex]x^4+5x^3-3x-15=x^3-3\times g(x)+0[/tex]
So, our equation becomes
[tex]g(x)\\\\=\frac{x^4+5x^3-3x-15}{x^3-3}\\\\=x+5[/tex]
So, our required polynomial is given by
[tex]x+5[/tex]
Answer:
Dividend
[tex]=x^4 + 5 x^3 - 3 x - 15[/tex]
Divisor
[tex]=x^3-3[/tex]
The rule of division of polynomial which is same as division of real numbers states that
Dividend = Divisor × Quotient + Remainder
The division process is shown below.
Quotient = x+5
Remainder =0
