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
This website will show the principles of solving Math problems in Arithmetic, Algebra, Plane Geometry, Solid Geometry, Analytic Geometry, Trigonometry, Differential Calculus, Integral Calculus, Statistics, Differential Equations, Physics, Mechanics, Strength of Materials, and Chemical Engineering Math that we are using anywhere in everyday life. This website is also about the derivation of common formulas and equations. (Founded on September 28, 2012 in Newark, California, USA)
Monday, October 21, 2013
Sunday, October 20, 2013
Special Products - Factoring, 9
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
"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
Saturday, October 19, 2013
Special Products - Factoring, 8
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
"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
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