Question
Answer
$$2.924751e-5(x+19)(x+7)(x-2)(x-2)(x-10)=-5x^5-60x^4+935x^3+3790x^2+2e-24060x+26600$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2.924751e-5(x+19)(x+7)(x-2)(x-2)(x-10)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2e-(5x+95)(x+7)(x-2)(x-2)(x-10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2e-(5x^2+35x+95x+665)(x-2)(x-2)(x-10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2e-(5x^2+130x+665)(x-2)(x-2)(x-10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2e-(5x^3-10x^2+130x^2-260x+665x-1330)(x-2)(x-10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}2e-(5x^3+120x^2+405x-1330)(x-2)(x-10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}2e-(5x^4+110x^3+165x^2-2140x+2660)(x-10) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle8}{\textcircled {8}} \htmlClass{explanationCircle explanationCircle9}{\textcircled {9}} } }}}2e-(5x^5+60x^4-935x^3-3790x^2+24060x-26600) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle10}{\textcircled {10}} } }}}2e-5x^5-60x^4+935x^3+3790x^2-24060x+26600 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle11}{\textcircled {11}} } }}}-5x^5-60x^4+935x^3+3790x^2+2e-24060x+26600\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{5} $ by $ \left( x+19\right) $ $$ \color{blue}{5} \cdot \left( x+19\right) = 5x+95 $$ |
| ② | Multiply each term of $ \left( \color{blue}{5x+95}\right) $ by each term in $ \left( x+7\right) $. $$ \left( \color{blue}{5x+95}\right) \cdot \left( x+7\right) = 5x^2+35x+95x+665 $$ |
| ③ | Combine like terms: $$ 5x^2+ \color{blue}{35x} + \color{blue}{95x} +665 = 5x^2+ \color{blue}{130x} +665 $$ |
| ④ | Multiply each term of $ \left( \color{blue}{5x^2+130x+665}\right) $ by each term in $ \left( x-2\right) $. $$ \left( \color{blue}{5x^2+130x+665}\right) \cdot \left( x-2\right) = 5x^3-10x^2+130x^2-260x+665x-1330 $$ |
| ⑤ | Combine like terms: $$ 5x^3 \color{blue}{-10x^2} + \color{blue}{130x^2} \color{red}{-260x} + \color{red}{665x} -1330 = 5x^3+ \color{blue}{120x^2} + \color{red}{405x} -1330 $$ |
| ⑥ | Multiply each term of $ \left( \color{blue}{5x^3+120x^2+405x-1330}\right) $ by each term in $ \left( x-2\right) $. $$ \left( \color{blue}{5x^3+120x^2+405x-1330}\right) \cdot \left( x-2\right) = 5x^4-10x^3+120x^3-240x^2+405x^2-810x-1330x+2660 $$ |
| ⑦ | Combine like terms: $$ 5x^4 \color{blue}{-10x^3} + \color{blue}{120x^3} \color{red}{-240x^2} + \color{red}{405x^2} \color{green}{-810x} \color{green}{-1330x} +2660 = \\ = 5x^4+ \color{blue}{110x^3} + \color{red}{165x^2} \color{green}{-2140x} +2660 $$ |
| ⑧ | Multiply each term of $ \left( \color{blue}{5x^4+110x^3+165x^2-2140x+2660}\right) $ by each term in $ \left( x-10\right) $. $$ \left( \color{blue}{5x^4+110x^3+165x^2-2140x+2660}\right) \cdot \left( x-10\right) = \\ = 5x^5-50x^4+110x^4-1100x^3+165x^3-1650x^2-2140x^2+21400x+2660x-26600 $$ |
| ⑨ | Combine like terms: $$ 5x^5 \color{blue}{-50x^4} + \color{blue}{110x^4} \color{red}{-1100x^3} + \color{red}{165x^3} \color{green}{-1650x^2} \color{green}{-2140x^2} + \color{orange}{21400x} + \color{orange}{2660x} -26600 = \\ = 5x^5+ \color{blue}{60x^4} \color{red}{-935x^3} \color{green}{-3790x^2} + \color{orange}{24060x} -26600 $$ |
| ⑩ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 5x^5+60x^4-935x^3-3790x^2+24060x-26600 \right) = -5x^5-60x^4+935x^3+3790x^2-24060x+26600 $$ |
| ⑪ | Combine like terms: $$ -5x^5-60x^4+935x^3+3790x^2+2e-24060x+26600 = -5x^5-60x^4+935x^3+3790x^2+2e-24060x+26600 $$ |
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