Question

The quotient of (x4 + 5x3 – 3x – 15) and a polynomial is (x3 – 3). What is the polynomial?

Answer 1

Answer:

Dividend

 $=x^4 + 5 x^3 - 3 x - 15$

Divisor

$=x^3-3$

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

Answer 2

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

$x+5$