Answer:
e) Unfactorable
Step-by-step explanation:
When we factor a quadratic expression in the form ax² + bx + c, we are seeking two linear factors of the form (mx + p)(nx + q) where m, n, p, and q are integers.
To do this, we need to find two numbers that multiply to the product of 'a' and 'c' and add up to 'b'. These numbers will be used to split the middle term when factoring.
In the case of m² - 5m - 35, the constant term is c = -35 and b = -5, so we are looking for two integers whose product is -35 and whose sum is -5.
The factor pairs of -35 are:
As none of these factors pairs sum to -5, there are no such pairs of integers that satisfy these conditions. Therefore, this suggests that the given quadratic cannot be factored into two linear factors with integer coefficients. Hence, the quadratic is:
[tex]\Large\boxed{\boxed{\sf Unfactorable}}[/tex]
