Question

can someone explain why x^2+28+60 is prime? i did the work and i dont think it is.

Answer 1

\[x^2 +28 + 60 = x^2 + 88\]is prime.

More seriously, though, if your quadratic is not prime and you did the work, then you came up with a proposed factorization that reduces it for example: (x+20)(x+3) = x^2 + 23x + 60. What did you find?

Answer 2

im doing factoring not quadratics. i just figured out why its prime, but thanks anyways

Answer 3

no probs. i look whether the discriminant (28)^2 - 4(1)(60) is a perfect square, but there are other ways to check whether it is prime.

Answer 4

in both cases , it is not necessary that the number is prime for all values of x

Answer 5

@sam_unleashed: Both \[x^2+88\] and \[x^2+28x+60\]are prime, which is jargon for saying that they can't be factored (over the rational number field Q).

http://en.wikipedia.org/wiki/Factorization_of_polynomials

For those who are so inclined, completing the square coughs up: \[x^2+88 = (x-2i\sqrt{22})(x+2i\sqrt{22})\]and\[x^2+28x+60=(x-14-2\sqrt{34})(x-14+2\sqrt{34})\]

Answer 6

my question is ...x is not a value its variable...
so different values of x make the number prime or non prime..

Answer 7

The word "prime" means many things. For example, the apostrophe mark ' is referred to as prime. In psychology a trigger event can be a prime. To a butcher, a rib can be prime. @wowbriana wasn't asking whether (x^2+28x+60) ever added up to a "prime_number," she was asking whether (x^2+28x+60) was itself a "prime_polynomial."

This is a new usage of the word "Prime" that starts appearing in Algebra 2.
\[(x+4)\]is an example of a prime.
\[(x+4)(x+8)\]is not prime, because it is the product of two pieces, (x+4) and (x+8) ... It can be factored into two pieces. Being a prime_polynomial is an inherent property of the polynomial itself, and it ignores whether or not any coefficient "4" for example is a prime_number.