"Published in Suisun City, California, USA"
Find the factors for
Solution:
Consider the given equation above
If you think that the above equation cannot be factored, then you must consider first the investigation of each terms whether they can be factored or not. The variables at the first and last terms are perfect square. Since the last term is negative, then obviously we cannot take a square root of a negative number and hence, the given equation is not a perfect trinomial square. We can check the above equation using discriminant if it can be factored or not as follows
where a, b, and c are the coefficients of a trinomial. Now, let's check the given equation as follows
Since the value of discriminant is a whole number, then the given equation can be factored. Next, we have to think the factors of the first and last terms so that when we add the product of two factors of the first and last terms, it will be the same as the middle term. The factors of the first term are 1, 15, 3, and 5. The factors of the last term are 1, 15, 3, and 5. Since the last term is negative, then one of the two factors must be negative. We need to do the trial and error in assigning the factors as follows:
Trial 1: Use 1 and 15 for the first term and 3 and -5 for the last term.
The middle term is (1)(-5) + (3)(15) = -5 + 45 = 40.
Trial 2: Use 5 and 3 for the first term and 3 and -5 for the last term.
The middle term is (5)(-5) + (3)(3) = -25 + 9 = -16.
Since the middle term is -16ab which is exactly the same as the answer above, then the factors of the given equation are
