Chapter 7.2, Problem 26E

To determine

To calculate: The product of the polynomial $(z-\frac{5}{3})(z-\frac{2}{3})$ using FOIL (Firsts Outsides Insides Lasts) method.

Answer to Problem 26E

The product of the polynomial $(z-\frac{5}{3})(z-\frac{2}{3})$ using FOIL method is $z^2-\frac{7z}{3}+\frac{10}{9}$

Explanation of Solution

Given information:

The given polynomial is $(z-\frac{5}{3})(z-\frac{2}{3})$ , where ‘z’ is a variable

Calculation:

On multiplying first term of both binomials,

  $z\times z=z^2$

On multiplying outside terms of each binomial,

  $z\times (-\frac{2}{3})=-\frac{2z}{3}$

On multiplying inside terms of both binomials,

  $(-\frac{5}{3})\times z=-\frac{5z}{3}$

On multiplying last terms of each binomial,

  $(-\frac{5}{3})\times (-\frac{2}{3})=\frac{10}{9}$

On adding all these terms,

  $(z-\frac{5}{3})(z-\frac{2}{3})$$=z^2-\frac{2z}{3}-\frac{5z}{3}+\frac{10}{9}$

  $=z^2-\frac{7z}{3}+\frac{10}{9}$

Thus, the required product of the given polynomial is $z^2-\frac{7z}{3}+\frac{10}{9}$ .