Question

Explain, in complete sentences, why the expression x2 + 28x + 60 is prime.

Answer 1

@Hero @amistre64

Answer 2

what do we call things that are prime? think of a prime number, what property does it hold that makes it prime?

Answer 3

Because you can't factor it, in order to factor that polynomial you'd have to find 2 numbers that multiply to 60 and add to 28, which there are none.

Answer 4

if you know about determinants, then you will be able to assess if its prime or not

Answer 5

There ain't no factors of 60 that sum to 28.

Is that a sentence?

Answer 6

might be discriminants .... to many 'd' words to keep track of :)

Answer 7

@amistre64

a prime number is 5

Answer 8

irrational roots are still factors tho

Answer 9

why is 5 prime?

Answer 10

because it can only be divided evenly by 1 or 5

Answer 11

@amistre64

Answer 12

right, it cant be factored into smaller parts.

with polymonials, they are prime if they have no 'real' valued roots .... if they possess complex roots, they are not factorable across the reals

Answer 13

your poly is prime if and only if it has no 'real' roots. and that can be determined by the discriminant: b^2 -4ac = D

if D >=0 it has real roots
if D < 0 it has no real roots

Answer 14

take x^2+4 as an example:

(x+2i)(x-2i) = x^2 -(2i)^2 = x^2 + 4, it has factors that are complex, not real.

0^2 -4(1)(1) = -4, -4<0 therefore x^2 + 4 is prime

Answer 15

Thank You for helping me @amistre64

Answer 16

youre welcome