Question

The Divisor, Quotient and Remainder of a Polynomial are
(4x-1), (4x+1) and 4 respectively. Then, the polynomial is​

Answer 1

Step-by-step explanation:

Given,

Divisor = (4x-1)

Quotient = (4x+1)

Remainder = 4

We know,

Polynomial = Divisor × Quotient + Remainder

Putting values,

$(4x-1) \times (4x+1) + 4\\ \\ \implies 16x^2-1+4 \qquad \because (a+b) \times (a-b)=a^2-b^2\\ \\ \implies 16x^2+3 \\ \\ \bf \therefore The\ polynomial\ is\ 16x^2+3.$

Answer 2

$\bf{\huge{\boxed{\underline {\underline {\mathcal{\blue{Answer}}}}}}}$

Given:

Divisor = 4x - 1

Quotient = 4x + 1

Remainder = 4

Literally my favourite formula and the easiest one ever I studied xD even if you ask me in sleep I will tell you the formula, I'm a scholar, I know that xD

Dividend = divisor × Quotient + Remainder

Put the values of the dividend, divisor, quotient and the remainder in the above formula.

But here just a minute change, as the question is about finding the polynomial we will replace the word dividend by polynomial in the formula.

Polynomial = divisor × Quotient + Remainder

( 4x - 1 ) (4x + 1 ) + 4

4x ( 4x + 1) -1 (4x +1) + 4 $\bf\underbrace{Multiplying\: the \:brackets}$

16x² + 4x - 4x - 1 + 4

16x² -1 + 4 $\bf\underbrace{Like\: terms with \:opposite \:signs \:gets\:cancelled}$

16x² + 3

$\bf{\large{\boxed{\underline {Polynomial = 16x^2 + 3}}}}}$