The common term for that phrase is the verb 'factor'. Factoring is the reverse of expanding (aka: multiplying out, or 'foiling, in this instance').
The given quadratic polynomial does not factor nicely. The factorization is:
(x + 1 - i)(x + 1 + i)
where symbol i represents the square root of -1 (aka the imaginary unit).
There's a shortcut for determining whether a quadratic polynomial (Ax^2+Bx+C) factors nicely. Determine its Discriminant (B^2-4AC). If the Discriminant is not a perfect square, then the polynomial does not factor nicely.
Last edited by mmm4444bot; 01-22-2018 at 01:53 AM. Reason: used \text{} to prevent auto-linking from interfering with my blood!!
"English is the most ambiguous language in the world." ~ Yours Truly, 1969
Thanks for answering.
Is there a way to find the lowest common denominator to factor?
OK, I will try and come up with an example.
X^2+40X+6
X^2, 40, and 6 all have the number 2 in common. X^2 is just X times X, so you really don't need to manipulate anything there.
Could you use 2 to find the lowest common denominator to factor the rest of the equation out?
You may mean "greatest common factor" rather than "lowest common denominator".
But 2 is not a factor of x^2; it's an exponent, which is an entirely different thing.
This polynomial, like the first, can't be factored over the integers (that is, factored into factors containing only integers).
Thanks, I think I have the basic concept down now.
You have to take the equation as a whole and you can't split it up into different sections. That is what I was trying to figure out.
To say it better, you can't really 'mix and match' with addition and multiplication to find a greatest common factor.
But I was thinking along these lines:
X^2+40X+6
x^2+2(20x+3)
But I don't think this actually changes the equation to the point that you can Factor from that point...
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