Question
Multiply polynomial $ \, \color{blue}{ x+3 } \, $ by $ \, \color{orangered}{ x^3-5 }$.
Answer
$$ \left( \color{blue}{x+3} \right) \cdot \left( \color{orangered}{x^3-5} \right) = x^4+3x^3-5x-15 $$
Explanation
In this example we are multiplying two binomials so FOIL method can be used.
$$ \begin{aligned} \left( \color{blue}{ x+3}\right) \cdot \left( \color{orangered}{ x^3-5}\right) &= \underbrace{ \color{blue}{x} \cdot \color{orangered}{x^3} }_{\text{FIRST}} + \underbrace{ \color{blue}{x} \cdot \left( \color{orangered}{-5} \right) }_{\text{OUTER}} + \underbrace{ \color{blue}{3} \cdot \color{orangered}{x^3} }_{\text{INNER}} + \underbrace{ \color{blue}{3} \cdot \left( \color{orangered}{-5} \right) }_{\text{LAST}} = \\ &= x^4 + \left( -5x\right) + 3x^3 + \left( -15\right) = \\ &= x^4 + \left( -5x\right) + 3x^3 + \left( -15\right) = \\ &= x^4+3x^3-5x-15; \end{aligned} $$This page was created using
Polynomial Operations Calculator