Category: Algebra
"Published in Suisun City, California, USA"
Find the factors for
Solution:
Consider the given equation above
The given equation is also a trinomial where (x + y) is considered as a single variable. It is not a perfect trinomial square because the first and last terms are not perfect 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 last term so
that we add the two factors, it will be the same as the middle term. The
possible factors of the last term are 1, 2, -1 and -2. If the middle term is -3, then
the factors must be -1 and -2. When you add -1 and -2, it will give us
-3. Therefore, the factors of the above equation are
Category: Algebra
"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
Category: Algebra
"Published in Newark, 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 last term so that we add the two factors, it will be the same as the middle term. The possible factors of the last term are 1, -1, 135, -135, 5, -5, 27, -27, 3, -3, 45, -45, 9, -9, 15, and -15. If the middle term is -134, then the factors must be 1 and -135. When you add 1 and -135, it will give us -134. Therefore, the factors of the above equation are
