Chapter 6, Problem 7PT

To determine

To Find:

  $(f\cdot g)(x)$

Answer to Problem 7PT

  $3x^3-4x^2-x+2$

Explanation of Solution

Given Information:

The functions are :

  $\begin{array}{l}f(x)=3x+2\\ g(x)=x^2-2x+1\end{array}$

Formula used :

• For any two functions f and g :

  $(f\cdot g)(x)=f(x)\cdot g(x)$

• Distributive property of multiplication over addition:

  $a(b+c)=ab+ac$

Calculation:

  $\begin{array}{l}Given\\ f(x)=3x+2\\ g(x)=x^2-2x+1\\ (f\cdot g)(x)\\ =f(x)\cdot g(x)\\ =(3x+2)\cdot (x^2-2x+1)\\ =3x(x^2-2x+1)+2(x^2-2x+1)\mathrm{....}[\text{distributive property]}\\ =3x^3-6x^2+3x+2x^2-4x+\mathrm{2.......}[\text{distributive property]}\\ =3x^3+x^2(-6+2)+x(3-4)+\mathrm{2.....}[\text{add like terms]}\\ \text{= }3x^3-4x^2-x+\mathrm{2.........................}\left[\begin{array}{l}\text{always write the answer starting with the term }\\ \text{that has the hightest exponent value, and go on }\\ \text{in a decending order of the power}\end{array}\right]\end{array}$