Multiply polynomial $ \, \color{blue}{ 3x-4 } \, $ by $ \, \color{orangered}{ 5+3x-4x }$.

$$ \left( \color{blue}{3x-4} \right) \cdot \left( \color{orangered}{5+3x-4x} \right) = -3x^2+19x-20 $$

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

$$ \begin{aligned} P(x) &= 3x-4 \\ Q(x) &= -x+5 \\ \end{aligned} $$

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

$$ \begin{aligned} \left( \color{blue}{ 3x-4}\right) \cdot \left( \color{orangered}{ -x+5}\right) &= \underbrace{ \color{blue}{3x} \cdot \left( \color{orangered}{-x} \right) }_{\text{FIRST}} + \underbrace{ \color{blue}{3x} \cdot \color{orangered}{5} }_{\text{OUTER}} + \underbrace{ \left( \color{blue}{-4} \right) \cdot \left( \color{orangered}{-x} \right) }_{\text{INNER}} + \underbrace{ \left( \color{blue}{-4} \right) \cdot \color{orangered}{5} }_{\text{LAST}} = \\ &= -3x^2 + 15x + 4x + \left( -20\right) = \\ &= -3x^2 + 15x + 4x + \left( -20\right) = \\ &= -3x^2+19x-20; \end{aligned} $$

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