# If a polynomial p(x) is divided with a polynomial (x

If a polynomial p(x) is divided with a polynomial (x + 3) using long division and the quotient is $2{x}^{2}x+1$. Find p(x).
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Step 1: Given that:
If a polynomial p(x) is divided with a polynomial (x + 3) using long division and the quotient is $2{x}^{2}+x+1$. Find p(x).
Step 2: Formula Used:
Dividend = Divisior $×$ Quotient + Remainder
or
$p\left(x\right)=g\left(x\right)×q\left(x\right)+r\left(x\right)$
Step 3: Calculation
We have,
g(x)=x+3
$q\left(x\right)=2{x}^{2}+x+1$
r(x)=0
So by the formula used we have,
$p\left(x\right)=\left(x+3\right)\left(2{x}^{2}+x+1\right)+0$
$=2{x}^{3}+{x}^{2}+x+6{x}^{2}+3x+3$
$=2{x}^{3}+7{x}^{2}+4x+3$