#### Answer

The expression for the width of a rectangle is $3x^2+5x+2$.

#### Work Step by Step

Formula of the area: $A=lw$
The length is: $l=4x+1$
The area is: $A=12x^3+23x^2+13x+2$
This gives: $12x^3+23x^2+13x+2=(4x+1).w$
$w=\frac{12x^3+23x^2+13x+2}{4x+1}$
$3x^2+5x+2$
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$4x+1 ) 12x^3+23x^2+13x+2$
$-12x^3-3x^2$
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$20x^2+13x$
$-20x^2-5x$
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$8x+2$
$-8x-2$
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$0$
Hence, the expression for the width of a rectangle is $3x^2+5x+2$.