The following exercises are geometric in nature and lead to polynomial models. Solve each problem. A certain right triangle has area 84 in.². One leg of the triangle measures 1 in. less than the hypotenuse. Let x represent the length of the hypotenuse. Express the length of the leg mentioned above in terms of x. Give the domain of x.

Solve each problem. A comprehensive graph of ƒ(x)=x⁴-7x³+18x²-22x+12 is shown in the two screens, along with displays of the two real zeros. Find the two remaining nonreal complex zeros.

Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient. $f\(\left\)(x\(\right\))=2+x$

Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient. $f\(\left\)(x\(\right\))=3x^2+5x+2$

Determine the end behavior of the given polynomial function. $f\(\left\)(x\(\right\))=x^2+4x+x+7x^3$

Match the given polynomial function to its graph based on end behavior. $f\(\left\)(x\(\right\))=-2x^3+x^2+1$