48x^2y + 20xz + 12xy + 5z
xy - 3x – 8y + 24
are these Prime expressions or not?
Each expression has two factors.
i do not understand?
prime expressions cannot have factors. The prime number 13 has no factors except itself. 5z has two factors, 5, and z.
To determine whether an expression is prime or not, we need to understand the concept of prime expressions. In mathematics, a prime expression refers to an algebraic expression that cannot be factored any further. If an expression can be simplified or factored into smaller expressions, then it is not prime.
Let's analyze each expression one by one:
1. 48x^2y + 20xz + 12xy + 5z
This expression contains four terms. To check if it can be factored further, we look for any common factors.
- We can factor out the greatest common factor (GCF) from each term. The GCF of all terms is 1 (which is the smallest positive integer), so we cannot factor it out further.
Therefore, the first expression, 48x^2y + 20xz + 12xy + 5z, is prime.
2. xy - 3x – 8y + 24
This expression also contains four terms. Again, let's check if we can find any common factors.
- We can factor out "x" from the first two terms, and "8" from the last term.
- The remaining terms do not have any common factors.
After factoring, the expression becomes: x(y - 3) - 8(y - 3)
Now we can see that the expression can be further factored into two binomial expressions,
(y - 3)(x - 8).
Therefore, the second expression, xy - 3x – 8y + 24, is not prime.
In conclusion:
- The expression 48x^2y + 20xz + 12xy + 5z is prime.
- The expression xy - 3x – 8y + 24 is not prime.