Given:
Length of the prism, L = x + 2
Width of prism, W = x + 4
Height of prism, H = x
To find the surface area, use the formula already given:
Surface Area = 2LW + 2LH + 2WH
Input the values into the formula:
Surface Area = 2(x+2)(x+4) + 2(x+2)(x) + 2(x+4)(x)
Expand the parentheses:
[tex]2(x^2+6x+8)\text{ + 2(x}^2+2x)+2(x^2+4x)[/tex]
Use distributive property to multiply:
[tex]2x^2+12x+16+2x^2+4x+2x^2+8x[/tex]
Collect like terms and evaluate:
[tex]\begin{gathered} 2x^2+2x^2+2x^2+12x+4x+8x+16 \\ \\ =6x^2+24x+16 \end{gathered}[/tex]
Therefore, the surface area of the rectangular prism as a polynomial in standard form is:
[tex]6x^2+24x+16[/tex]
ANSWER:
[tex]6x^2+24x+16[/tex]
