Step 1: First we have to write polynomials in descending order.

$$ \begin{aligned} P(x) &= -17x+18 \\ Q(x) &= 12x+26 \\ \end{aligned} $$

In this example we are multiplying two binomials so FOIL method can be used.

$$ \begin{aligned} \left( \color{blue}{ -17x+18}\right) \cdot \left( \color{orangered}{ 12x+26}\right) &= \underbrace{ \left( \color{blue}{-17x} \right) \cdot \color{orangered}{12x} }_{\text{FIRST}} + \underbrace{ \left( \color{blue}{-17x} \right) \cdot \color{orangered}{26} }_{\text{OUTER}} + \underbrace{ \color{blue}{18} \cdot \color{orangered}{12x} }_{\text{INNER}} + \underbrace{ \color{blue}{18} \cdot \color{orangered}{26} }_{\text{LAST}} = \\ &= -204x^2 + \left( -442x\right) + 216x + 468 = \\ &= -204x^2 + \left( -442x\right) + 216x + 468 = \\ &= -204x^2-226x+468; \end{aligned} $$

Polynomial Operations Calculator