Chapter 8.3, Problem 30PPS

To determine

To find: The product $\left(6z^2-5z-2\right)\left(3z^3-2z-4\right)$

Answer to Problem 30PPS

  $18z^5-15z^4-18z^3-14z^2+24z+8$

Explanation of Solution

Given:

  $\left(6z^2-5z-2\right)\left(3z^3-2z-4\right)$

Calculation:

Multiply each term of the first polynomial with the each term of the second polynomial

  $\begin{array}{l}\left(6z^2-5z-2\right)\left(3z^3-2z-4\right)\\ =6z^2\cdot 3z^3+6z^2\cdot \left(-2z\right)+6z^2\cdot \left(-4\right)-5z\cdot 3z^3-5z\cdot \left(-2z\right)-5z\cdot \left(-4\right)-2\cdot 3z^3-2\cdot \left(-2z\right)-2\cdot \left(-4\right)\\ =18z^5-15z^4-12z^3-6z^3-24z^2+10z^2+20z+4z+8\\ =18z^5-15z^4-18z^3-14z^2+24z+8\end{array}$

So, the product of the polynomial is $18z^5-15z^4-18z^3-14z^2+24z+8$