How do you factor $x^6 + 2x^5 + 3x^4 + 6x^3$ ?

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Answer 1 · 2015-11-15T19:40:27

Separate out the common factor $x^3$ then factor by grouping to find:

$x^6+2x^5+3x^4+6x^3 = x^3(x^2+3)(x+2)$

$x^6+2x^5+3x^4+6x^3$

$=x^3(x^3+2x^2+3x+6)$

$=x^3((x^3+2x^2)+(3x+6))$

$=x^3(x^2(x+2)+3(x+2))$

$= x^3(x^2+3)(x+2)$

This has no simpler factors with Real coefficients since $x^2+3 >= 3 > 0$ for all $x in RR$

How do you factor x^6 + 2x^5 + 3x^4 + 6x^3x^6 + 2x^5 + 3x^4 + 6x^3?