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

1 answer:

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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Answer:

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Step-by-step explanation:

Lets say there's a number 'x' and there's an expression $(x^a)^b$ where 'a' & 'b' are also numbers , the simplified form of the expression is $x^{a \times b}$ .

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2 years ago

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Ipatiy [6.2K]

V=x^3+5x^2-57x-189
Width: W=(x+3) in = 15 in →x+3=15
Solving for x:
x+3-3=15-3→x=12

With x=12 the Volume would be:
V=(12)^3+5(12)^2-57(12)-189
V=1,728+5(144)-684-189
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V=1,575

V=W*D*H
Depth: D
Height: H
with H>D

V=1,575; W=15
Replacing in the equation above:
1,575=15*D*H
Dividing both sides by 15
1,575/15=(12*D*H)/15
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D<H
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If D=7→H=3*5→H=15

Answer: Option C. height: 21 in. depth: 5 in.

Please, see the attached file for another form to solve the problem