Factor into a product of binomials: if prime type prime.
X^2+12x+7
To factor the expression we need to find two binomials whose product is equal to the given expression.
We want the binomials to have the form (x + a)(x + b), where a and b are the unknown coefficients that we need to find.
The product of the binomials is:
(x + a)(x + b) = x^2 + (a + b)x + ab
We can see that the constant term in the expression is 7. Therefore, ab = 7.
Since 7 is a prime number, the possible values for a and b are 1 and 7, or -1 and -7 (or their negatives).
Now, we need to find the sum of the coefficients (a + b) in the expression. In this case, the sum is 12.
Testing the possible values for a and b:
For a = 1 and b = 7: (1 + 7) = 8, which is not equal to 12.
For a = -1 and b = -7: (-1 + -7) = -8, which is also not equal to 12.
Since neither of the possible values for a and b gives us the correct sum, it is not possible to factor the expression into a product of binomials if the coefficient is prime and the constant term is prime.