The discussion revolves around finding the real zeros of the polynomial function f(x) = x^3 + 5x^2 + 9x + 45 by factoring. Participants are examining the steps taken to factor the polynomial and the implications of those steps.
The conversation is focused on clarifying the factorization steps and addressing potential errors in terminology. Some participants are correcting each other regarding the classification of the GCF and discussing the implications of factoring out (x + 5).
There is mention of a possible typo in the factorization steps, and participants are reflecting on their understanding of the terminology used in the context of factoring polynomials.
There's an error in the step above.swatmedic05 said:f(x)=x^3+5x^2+9x+45
x^3+5x^2+9x+45=0
x^2(x+5)+9(x-5)=0
swatmedic05 said:(x^2+9)(x+5)=0
What happends to the (x+5)?
It was the greatest common factor, so it got factored out.What happened to the (x+5)?
It was the greatest linear factor. It is not a monomial, it is a binomial, just like [itex]x^2+ 9[/itex].eumyang said:[tex]\begin{aligned}<br /> x^3 + 5x^2 + 9x + 45 &= 0 \\<br /> x^2(x + 5) + 9(x + 5) &= 0 \\<br /> (x^2 + 9)(x + 5) &= 0<br /> \end{aligned}[/tex]
I'm assuming that the error pointed out above is just a typo, so I'll just fix it. As for
It was the greatest common monomial factor, so it got factored out.
Say you wanted to factor 16x - 28. The GCF is 4, and you could rewrite the expression as
4(4x) - 4(7),
and then factor out the 4 to get
4(4x - 7).
It's the same thing in your problem. The GCF is an expression: x + 5. You factor the x + 5 out in [tex]x^2 \bold{(x + 5)} + 9 \bold{(x + 5)} = 0[/tex] and you get [tex](x^2 + 9)(x + 5) = 0[/tex]. Maybe part of the confusion is that the GCF appears last instead of first?
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