Question

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

Answer 1

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`

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)* 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* g(x)+0`

So, our equation becomes

`g(x)\\\\=(x^4+5x^3-3x-15)/(x^3-3)\\\\=x+5`

So, our required polynomial is given by

`x+5`