Question
Answer
$$(-x+5)(x^3+6x^2+11x+30)=-x^4-x^3+19x^2+25x+150$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-x+5)(x^3+6x^2+11x+30)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-x^4-x^3+19x^2+25x+150\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{-x+5}\right) $ by each term in $ \left( x^3+6x^2+11x+30\right) $. $$ \left( \color{blue}{-x+5}\right) \cdot \left( x^3+6x^2+11x+30\right) = -x^4-6x^3-11x^2-30x+5x^3+30x^2+55x+150 $$ |
| ② | Combine like terms: $$ -x^4 \color{blue}{-6x^3} \color{red}{-11x^2} \color{green}{-30x} + \color{blue}{5x^3} + \color{red}{30x^2} + \color{green}{55x} +150 = -x^4 \color{blue}{-x^3} + \color{red}{19x^2} + \color{green}{25x} +150 $$ |
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