from the expression below, which one is not factorable?
1)x^2+4x+6
2) 3ab^2-16a
3)x^2-441
4)4x^2+19x-5
I thought the answer was 2) b is not in the second part of the equation(the 16a)
Is this correct?
Thanks for checking my work
To determine whether an expression is factorable or not, we need to look for a common factor or a pattern that can be factored out. Let's analyze each expression:
1) x^2 + 4x + 6:
This expression is a quadratic trinomial, and we can use the quadratic formula or factorization methods to determine if it can be factored. In this case, the expression cannot be factored using integers or rational numbers, so it is not factorable.
2) 3ab^2 - 16a:
In this expression, we can see that there is a common factor of 'a.' Factoring out 'a,' we get: a(3b^2 - 16). Therefore, this expression is indeed factorable.
3) x^2 - 441:
This expression is a difference of squares, which is a special case of factoring. It can be factored as (x - 21)(x + 21). Hence, this expression is factorable.
4) 4x^2 + 19x - 5:
In this case, the expression is also a quadratic trinomial. We can use the quadratic formula or factorization methods. We can find the factors of this expression by finding the product of 'a' and 'c' and looking for two numbers whose sum is equal to 'b'. However, since there is no such combination of two numbers, we cannot factor this expression using integers or rational numbers. Hence, this expression is not factorable.
Based on the analysis above, the correct answer is 1) x^2 + 4x + 6, as it is the only expression that is not factorable.