Category: Algebra
"Published in Newark, California, USA"
Find the factors for
Solution:
Consider the given equation above
If you will examine the given equation, each terms are perfect cube. (a + b) is considered as a single variable. The given equation can be factored by the sum and difference of two cubes. Therefore, the factors are
Category: Algebra
"Published in Newark, California, USA"
Find the factors for
Solution:
Consider the given equation above
If you will examine the equation above, there's a common factor which is a. Take out their common factor as follows
Since each terms in the parenthesis are perfect cube, then we can factor the grouped terms as the sum and difference of two cubes. Therefore, the factors are
Category: Algebra
"Published in Newark, California, USA"
Find the factors for
Solution:
Consider the given equation above
The
given equation has two variables, x and (a + 3b). (a + 3b) 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 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, 12, 2, 6, 3, and 4. 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 12 for the first term and 1 and -15 for the last term.
The middle term is (1)(-15) + (1)(12) = -15 + 12 = -3.
Trial 2: Use 2 and 6 for the first term and 3 and -5 for the last term.
The middle term is (2)(-5) + (3)(6) = -10 + 18 = 8.
Trial 3: Use 4 and 3 for the first term and 3 and -5 for the last term.
The middle term is (4)(-5) + (3)(3) = -20 + 9 = -11.
Since the middle term is -11x(a + 3b) which is exactly the same as the answer above, then the factors of the given equation are
