Which statement about the polynomial function g(x) is true?
if all rational roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.
if all roots of g(x) = 0 are integers, the leading coefficient of g(x) must be 1.
if the leading coefficient of g(x) is 1, all rational roots of g(x) = 0 must be integers.
if the leading coefficient of g(x) is 1, all roots of g(x) = 0 must be integers.

The correct answer is:

If the leading coefficient of g(x) is 1, all rational roots of g(x) = 0 must be integers.

Explanation:

The Rational Root Theorem states:

If P(x) is a polynomial with integer coefficients and if p/q is a zero of P(x) (P(p/q)=0), then p is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P(x).

If p(x) is an nth degree monic polynomial (has a leading coefficient of 1) with integer coefficients, then a consequence of the Rational Root Theorem is:

If p(x) has at least one rational root, then each of its rational roots or zeros, must be an integer.

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2