Question

When a polynomial P(x) is divided by $x+3$ the quotient and remainder are $2x+1$ and 4 respectively, find the polynomial P(x).

• A. $2x^2+7x+7$
• B. $x^2–7x+50$
• C.
  $x^2–15x+50$
• D. $x^2–15x+50$

Answer 1

The correct option is A $2x^2+7x+7$

1 We have given :- divisor = x+3

Quotient = 2x+1

Remainder = 4

To Find:- Polynomial(We can say it as dividend)

Using formula :-

Dividend = Divisor × Quotient +Remainder.
Put value in the above formula

Here, Polynomial= $(x+3)\times (2x+1)+4$

$x(2x+1)+3(2x+1)+4$

$2x²+x+6x+3+4$

$2x²+7x+7$

Therefore, the required polynomial is $2x²+7x+7$