An area of a rectangle is represented by the function p(x)=3x^3+14x^2-23x+6. The width of the rectangle is represented as x + 6 . What is the expression for the length of the rectangle?3x^2-4x+13x^2+4x-13x^2-4x-13x^2+4x+1

Answer:[tex]3x^{2}-4x+1[/tex]Step-by-step explanation:Let [tex]l[/tex] be the length of the rectangle.Let [tex]b[/tex] be the breadth of the rectangle.The area of the rectangle with length [tex]l[/tex] an breadth [tex]b[/tex] is given by [tex]l\times b[/tex]Given that [tex]b=x+6[/tex]Given that area is [tex]3x^{3}+14x^{2}-23x+6[/tex]Option A:[tex]lb=(x+6)(3x^{2}-4x+1)=3x^{3}-4x^{2}+x+18x^{2}-24x+6=3x^{3}+14x^{2}-23x+6[/tex]This is the area given.So,option A is correct.Option B:[tex]lb=(x+6)(3x^{2}+4x-1)=3x^{3}+4x^{2}-x+18x^{2}+24x-6=3x^{3}+22x^{2}+23x-6[/tex]But this is not the area given.So,option B is wrong.Option C:[tex]lb=(x+6)(3x^{2}-4x-1)=3x^{3}-4x^{2}-x+18x^{2}-24x-6=3x^{3}+14x^{2}-25x-6[/tex]But this is not the area given.So,option C is wrong.Option D:[tex]lb=(x+6)(3x^{2}+4x+1)=3x^{3}+4x^{2}-x+18x^{2}-24x-6=3x^{3}+14x^{2}-25x-6[/tex]But this is not the area given.So,option D is wrong.