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FromTheMoon [43]
2 years ago
15

X^3-2x^2+5x-10=0 how do you solve or factor this polynomial?

Mathematics
1 answer:
pshichka [43]2 years ago
7 0

\bf x^3-2x^2+5x-10=0\implies \stackrel{\textit{doing some grouping}}{(x^3-2x^2)+(5x-10)}=0 \\\\\\ \stackrel{\textit{common factoring}}{x^2\underline{(x-2)}+5\underline{(x-2)}}=0\implies \stackrel{\textit{more common factoring}}{\underline{(x-2)}(x^2+5)}=0 \\\\[-0.35em] ~\dotfill\\\\ x-2=0\implies x=2~~~~\textit{\large\checkmark} \\\\[-0.35em] ~\dotfill\\\\ x^2+5=0\implies x^2=-5\implies x=\sqrt{-5}\implies x=i\sqrt{5}\quad \bigotimes

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The form (x - p)^2 = q is the form that completing the square will leave us with.

---Add 5 to both sides

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---Divide the b term by 2, and square it. Then, add that number to both sides.

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p = 4

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Hope this helps!! :)

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