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factor completely x^5-3x^3-2x^2+6

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factor completely x⁵−3x³−2x²+6

Solution

(x+√3)(x−√3)(x−³√2)(x²+³√2x+³√2²)

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x⁵−3x³−2x²+6

=(x⁵−3x³)+(−2x²+6)

Factor out x³ from x⁵−3x³: x³(x²−3)

Factor out −2 from −2x²+6: −2(x²−3)

=x³(x²−3)−2(x²−3)

Factor out common term x²−3

=(x²−3)(x³−2)

Factor x²−3: (x+√3)(x−√3)

=(x+√3)(x−√3)(x³−2)

Factor x³−2: (x−³√2)(x²+³√2x+(³√2)²)

=(x+√3)(x−√3)(x−³√2)(x²+³√2x+(³√2)²)

(³√2)²=2²³

=(x+√3)(x−√3)(x−³√2)(x²+³√2x+2²³)

2²³=³√2²

=(x+√3)(x−√3)(x−³√2)(x²+³√2x+³√2²)

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

factor completely x^5-3x^3-2x^2+6

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