Chapter 9.9, Problem 19PPS

To determine

Solve the function.

Answer to Problem 19PPS

  $-5x^3+18x^2-11x-8$

Explanation of Solution

Given Information: $f\left(x\right)=-x^2+2x+1$ , $g\left(x\right)=5x-8$ , $h\left(x\right)=-3x-3$ and $k\left(x\right)=5x^2$

Formula Used: $\left(f·g\right)\left(x\right)=f(x)·g\left(x\right)$

Calculation:

  $f\left(x\right)=-x^2+2x+1$ , $g\left(x\right)=5x-8$ , $h\left(x\right)=-3x-3$ and $k\left(x\right)=5x^2$

Now, Use formula

  $\left(f·g\right)\left(x\right)=f(x)·g\left(x\right)$

Now, put the value of $f(x)$ and $g(x)$

  $\left(f·g\right)\left(x\right)=\left(-x^2+2x+1\right)·\left(5x-8\right)$

Now,

  $\left(f·g\right)\left(x\right)=-5x^3+8x^2+10x^2-16x+5x-8$

Hence,

  $\left(f·g\right)\left(x\right)=-5x^3+18x^2-11x-8$