Question
Answer
$$(x-1)(3x^2-5x-1)=3x^3-8x^2+4x+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-1)(3x^2-5x-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3x^3-5x^2-x-3x^2+5x+1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3x^3-8x^2+4x+1\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-1}\right) $ by each term in $ \left( 3x^2-5x-1\right) $. $$ \left( \color{blue}{x-1}\right) \cdot \left( 3x^2-5x-1\right) = 3x^3-5x^2-x-3x^2+5x+1 $$ |
| ② | Combine like terms: $$ 3x^3 \color{blue}{-5x^2} \color{red}{-x} \color{blue}{-3x^2} + \color{red}{5x} +1 = 3x^3 \color{blue}{-8x^2} + \color{red}{4x} +1 $$ |
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