Newbie question: Is pulling out factors and dividing the same? Please explain the difference in the examples below.
Example:
$$2x-4 \to 2(x-2)$$
Is it the same as
$$4x^2 - 8x + 1 = 0$$
$$\frac{4x^2 - 8 }{4} = -\frac{1}{4} \implies x^2 - 2x = -\frac{1}{4}$$
Thanks
$\endgroup$2 Answers
$\begingroup$Factoring is used to simplify polynomials for easy handling on one side of an equation. While division is one that comes with a two-sided equation where if you can divide one side for say $x$, you can divide the other side also by $x$. If you can tell by your examples, you can apply what I have said thus far. Although they are very similar, they have one or two different properties.
Hope this helps!
$\endgroup$ $\begingroup$"Factor" and "divisor" are synonyms. They are exactly the same concept. You can factor both polynomials like $x^2+7x+6$ and integers like $5432$, and both are non-trivial, and both will yield a set of unique prime factors that can't be factored further.
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