Find the roots or use the shortcut... its your choise

Let length, breadth and height (or roots of the given polynomial) of the cuboid are $l, b$ and $h$ respectively.

Now, $A=2(lb+bh+hl)=2*167=334$ and $V=lbh=385$ .

So, $A+V+1010=334+385+1010=\boxed{1729}$ .

I think that it might be clearer if you said "surface area" of the cuboid rather than just "area"?

By Vieta's formula

$lb+bh+hl=167$

$A= 2(lb+bh+hl)=334$

$V=lbh=385$

$A+V+1010=334+385+1010=\boxed{1729}$

Alsro the polynomial can be factored by Synthetic Division

Let length be $l$ , breadth be $b$ and height be $h$ . The equation is

$ax³+bx²+cx+d=x³-23x²+167x-385= 0$

$a=1, b=-23, c=167, d=-385$

From the Vieta's Formula, we get

$lbh= \frac{-d}{a} = 385$

$lb+bh+lh= \frac{c}{a} = 167$

$2(lb+bh+lh) = 2 \times 167 = 334$

Now,

$A+V+1010 = 334 + 385 + 1010$

$= \boxed{1729}$

Let $(x-a)(x-b)(x-c)= x^3-23x^2+167x-385=0$

Expanding the first expression $x^3-(a+b+c)x^2+(ab+ac+bc)x-abc=0$

$A=2(ab+bc+ac)=334$

$V=abc =385$

Then $385+334+1010=1729$

Isn't the value of A a negative number? Since the sum of two roots are negative. Could someone please clarify? Thanks