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
Category: Algebra
"Published in Newark, California, USA"
Find the factors for
Solution:
Consider the given equation above
The first and
the last terms are both perfect squares. The middle term is twice the
product of the square roots of first and last terms. Let's check the
middle term as follows
Since the
middle term is exactly the same as the computation above, then the given
trinomial is a perfect trinomial square. If the middle term is
negative, then the square root of the last term must be negative.
Therefore, the factors are
Therefore, the factors are
Category: Algebra
"Published in Newark, California, USA"
Find the factors completely for
Solution:
Consider the given equation above
Take out their common factor, we have
Since the two grouped terms are the difference of two squares, then we need to factor the two grouped terms as follows
Therefore, the factors are
Category: Algebra
"Published in Newark, California, USA"
Find the factors for
Solution:
Consider the given equation above
The first and the last terms are both perfect squares. The middle term is twice the product of the square roots of first and last terms. Let's check the middle term as follows
Since the middle term is exactly the same as the computation above, then the given trinomial is a perfect trinomial square. If the middle term is negative, then the square root of the last term must be negative. Therefore, the factors are
Category: Algebra
"Published in Newark, California, USA"
Find the factors for
Solution:
Consider the given equation above
We can rewrite the above equation as
Since each term is a perfect square and the other term is negative, then the given binomial can be factored by the difference of two squares. Therefore, the factors are
The middle term that contains xc will be equal to zero.
Category: Algebra
"Published in Newark, California, USA"
Write the product as a group of two terms for
Solution:
Consider the given equation above
Since each factor consists of four terms, then it is a long method to get the product of two polynomials by using Distributive Property of Multiplication Over Addition. We can get the product of two polynomials above by grouping of two terms into one group. Let's group the above equation and then get the product as follows
Since (2x - 3y) and (a - b) are consider as one term, then we can apply the product of two binomials for the above equation as follows
Without expanding each grouped terms, the final answer is
