SOLUTION: which expression is prime number? a.x2+4x+3 b.x2+5x+6 c.x2+6+8 d.none of the above

Algebra ->  Algebra  -> Divisibility and Prime Numbers  -> Lessons -> SOLUTION: which expression is prime number? a.x2+4x+3 b.x2+5x+6 c.x2+6+8 d.none of the above      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 458820: which expression is prime number?
a.x2+4x+3
b.x2+5x+6
c.x2+6+8
d.none of the above
Found 2 solutions by MathLover1, richard1234:
Answer by MathLover1(6625) About Me  (Show Source):
You can put this solution on YOUR website!

A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself,
and it must be a whole number greater than 1.

The smallest twenty-five prime numbers (all the prime numbers under 100) are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

a.

x+=+%28-4+%2B-+sqrt%284%5E2-4%2A1%2A3+%29%29%2F%282%2A1%29+
x+=+%28-4+%2B-+sqrt%2816-12+%29%29%2F2+
x+=+%28-4+%2B-+sqrt%284+%29%29%2F2+
x+=+%28-4+%2B-+2%29%2F2+
solutions:
x+=+%28-4+%2B+2%29%2F2+
x+=+-2%2F2+
x+=+-1+
or
x+=+%28-4+-2%29%2F2+
x+=+-6%2F2+
x+=+-3+

b.
x%5E2%2B5x%2B6
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-5+%2B-+sqrt%28+5%5E2-4%2A1%2A6+%29%29%2F%282%2A1%29+
x+=+%28-5+%2B-+sqrt%28+25-24+%29%29%2F2+
x+=+%28-5+%2B-+sqrt%28+1+%29%29%2F2+
x+=+%28-5+%2B-+1%29%2F2+

x+=+%28-5+%2B+1%29%2F2+
x+=+-4%2F2+
x+=+-2+
or
x+=+%28-5+-+1%29%2F2+
x+=+-6%2F2+
x+=+-3+


c.
x%5E2%2B6%2B8
x%5E2%2B14=0
x%5E2=-14
x=sqrt%28-14%29
x=3.74%2Ai

so, the answer is: d.none of the above

Answer by richard1234(5390) About Me  (Show Source):
You can put this solution on YOUR website!
The phrase "prime number" is reserved only for positive integers, not polynomial expressions. However, if you mean "which expression is a *prime polynomial*" that makes more sense (prime polynomial is a polynomial that cannot be factored into linear factors with integer coefficients).

We can see that a and b factor to (x+1)(x+3) and (x+1)(x+5) respectively. I have to assume you mean x^2 + 6x + 8 for c), which factors to (x+2)(x+4). So the answer is d), none of the above.