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}
x^3 + 5x^2 + 9x + 45 &= 0 \\
x^2(x + 5) + 9(x + 5) &= 0 \\
(x^2 + 9)(x + 5) &= 0
\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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To find the real zeros of a function algebraically, you can set the function equal to zero and then solve for the variable using techniques such as factoring, the quadratic formula, or the rational root theorem.
Real zeros of a function are the values of the variable that make the function equal to zero. In other words, they are the x-values where the graph of the function crosses the x-axis.
Yes, a function can have multiple real zeros. For example, a quadratic function can have two real zeros, while a cubic function can have three real zeros.
You can check if your calculated zeros are correct by plugging them back into the original function and seeing if the result is equal to zero. Additionally, you can graph the function and see if the calculated zeros align with the x-intercepts.
There are a few shortcuts or tricks for finding real zeros of a function, such as using the graphing calculator to approximate the zeros or using the Descartes' Rule of Signs to estimate the number of real zeros. However, these techniques should not replace the algebraic methods for finding the exact real zeros.