Try all the factoring techniques that you have been taught. If none work then it is prime (cannot be factored),
try looking for (1) a greatest common factor
(2) special binomials ... difference of squares, difference (or sum) of cubes
(3) trinomal factoring techniques
(4) other polymonials look for grouping techniques.
If a number cannot be factored it is a prime number.
It is (x+4)(x+5) when factored
You can evaluate a polynomial, you can factorise a polynomial, you can solve a polynomial equation. But a polynomial is not a specific question so it cannot be answered.
15j2(j + 2)
If you mean: x2+3x+2 then it is (x+1)(x+2) when factored
You can't know if a general polynomial is in factored form.
If a number cannot be factored it is a prime number.
It is still called a polynomial.
A prime polynomial is a polynomial that cannot be factored into the product of two non-constant polynomials over its coefficient field. In other words, it has no divisors other than itself and the unit (constant) polynomials. For example, in the field of real numbers, (x^2 + 1) is a prime polynomial because it cannot be factored into real linear factors. Conversely, polynomials like (x^2 - 1) are not prime because they can be factored as ((x - 1)(x + 1)).
Too bad that's not a^2 - ab - 42b^2 That factors to (a + 6b)(a - 7b)
In that case, it may, or may not, be possible to factor it using non-integer coefficients.
Completely Factored
It can, so the question does not make sense.
It is (x+4)(x+5) when factored
5x(3x+4)
If there is no common factor then the polynomial cannot be factorised. If there is no common factor then the polynomial cannot be factorised. If there is no common factor then the polynomial cannot be factorised. If there is no common factor then the polynomial cannot be factorised.
You can evaluate a polynomial, you can factorise a polynomial, you can solve a polynomial equation. But a polynomial is not a specific question so it cannot be answered.