Factoring question

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Hey guys I have a question

y^5+16y^4+28y^3

=y^3(y+2)(y+14) or (y+14)(y^4+2y^3)

Do both of these answers work for the equation?The reason I'm asking is because I want to be sure before moving on with in the textbook.Even though both of the answers seem fine
I really don't want to move on without be 100 percent sure,thanks-).

 

[stapel]

Hey guys I have a question

y^5+16y^4+28y^3

=y^3(y+2)(y+14) or (y+14)(y^4+2y^3)

Do both of these answers work for the equation?

I'm not sure what you mean by "working for the equation", but I think you're asking if each of the factored expressions in your third line above are valid factorizations of the original expression. If so, then, yes, they are valid factorizations.

However, if you were instructed to "factor" or "factor completely", then the first of the two factorizations is correct.

 

[Ishuda]

Hey guys I have a question

y^5+16y^4+28y^3

=y^3(y+2)(y+14) or (y+14)(y^4+2y^3)

Do both of these answers work for the equation?The reason I'm asking is because I want to be sure before moving on with in the textbook.Even though both of the answers seem fine
I really don't want to move on without be 100 percent sure,thanks-).

Although both answers are correct, as bestellen said, when being asked to factor an expression what is generally meant is complete factorization. This means get the expression down to products of constants and linear products as much as possible. The 'as much as possible' also means with Real coefficients at this level of mathematics. So your expression would generally be factored as
y⁵+16y⁴+28y³ = y³(y+2)(y+14)
Had the expression been
2y³+8y²+4y+16
the factorization would have been
2(y²+2)(y+4)
since y²+2 can not be factored further with Real coefficients.