Math Is Fun Forum

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Show Trinomial Is Prime

I came across an interesting question in Section R.5 for which Sullivan does not provide a sample question for.

Show that x^2 + x + 1 is prime.

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Show Trinomial Is Prime

I came across an interesting question in Section R.5 for which Sullivan does not provide a sample question for.

Show that x^2 + x + 1 is prime.

has the book covered the quadratic formula yet?
if yes, then set equal to zero and show quadratic formula has no real solutions
if no, then use that x^2 = x*x and 1 = 1*1 so any factors have to be (x [sign] 1)
try (x - 1)(x - 1), (x + 1)(x + 1), and (x + 1)(x - 1)
when none of them works then quadratic is prime

Bob

Administrator

Registered: 2010-06-20

Posts: 10,196

Re: Show Trinomial Is Prime

Show that x^2 + x + 1 is prime.

Is this meaning for all x ∈ {+integers} x^2 + x + 1 is a prime number?

Counter example x = 18 gives 343 which is not prime.

So if the question doesn't mean this, what does it mean?

I've tried a number of reliable maths sites and none have a concept 'quadratic prime'.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Show Trinomial Is Prime

I've tried a number of reliable maths sites and none have a concept 'quadratic prime'.

i think it means prime polynomial
thats any polynomial that isn't factorable over the integers
so x^2+1 is prime, but x^2-1 isn't

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Show Trinomial Is Prime

I came across an interesting question in Section R.5 for which Sullivan does not provide a sample question for.

Show that x^2 + x + 1 is prime.

has the book covered the quadratic formula yet?
if yes, then set equal to zero and show quadratic formula has no real solutions
if no, then use that x^2 = x*x and 1 = 1*1 so any factors have to be (x [sign] 1)
try (x - 1)(x - 1), (x + 1)(x + 1), and (x + 1)(x - 1)
when none of them works then quadratic is prime

Let me see what I can do.

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Show Trinomial Is Prime

Show that x^2 + x + 1 is prime.

Is this meaning for all x ∈ {+integers} x^2 + x + 1 is a prime number?

Counter example x = 18 gives 343 which is not prime.

So if the question doesn't mean this, what does it mean?

I've tried a number of reliable maths sites and none have a concept 'quadratic prime'.

Bob

Michael Sullivan provided one sample using a binomial. I will post his example as a guide for you to figure out this trinomial on my next day off. Bob, keep in mind that Saturday is my Monday and it begins with a double shift. Tomorrow another double with 3 hours of sleep in between due to distance. Ever has an insane schedule like this?

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Show Trinomial Is Prime

I've tried a number of reliable maths sites and none have a concept 'quadratic prime'.

i think it means prime polynomial
thats any polynomial that isn't factorable over the integers
so x^2+1 is prime, but x^2-1 isn't

Michael Sullivan provided one sample using a binomial. I will post his example as a guide for you to figure out this trinomial on my next day off. Keep in mind that Saturday is my Monday and it begins with a double shift. Tomorrow another double with 3 hours of sleep in between due to distance. Ever has an insane schedule like this?