Category: Algebra
"Published in Newark, California, USA"
Find the factors for
Solution:
Consider the given equation above
If
you think that you cannot factor the given equation, then you're right
because there's no common factor at each terms. How about if you will
expand the given equation and combine similar terms, then we can factor
the resulting equation if possible? Let's expand the given equation, we
have
The above equation is already arranged according to descending power of x. In order to factor a polynomial using synthetic division, you must know the factors of the last term or coefficient. In this case, 27 is the last term. The factors of 27 are 1, -1, 3, -3, 9, -9, 27, and -27. Unfortunately, we cannot use synthetic division since all factors of 27 will give us a remainder.
Don't worry, we can do something for the above equation in order to get the factors. And so, consider again the above equation
Group the first two terms, we have
Remove x² from the group,
We can make the grouped terms into a perfect trinomial square. Divide the coefficient of the middle term which is 8 by 2 and then square it. In this case, we have to add and subtract 16 at the above equation, as follows
Group the next two terms, we have
Rewrite the first group as a square of a binomial and take out the common factor at the next group,
Did you notice that the resulting equation is a quadratic equation in terms of x(x + 4)? The factors of 27 are 3 and 9. Since the middle term is -12, then the factors of 27 must be -3 and -9. If you add -3 and -9, it will give us -12 which is the coefficient of the middle term. Therefore, the factors of the given 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)
Saturday, November 9, 2013
Friday, November 8, 2013
Special Products - Factoring, 28
Category: Algebra
"Published in Newark, California, USA"
Find the factors for
Solution:
Consider the given equation above
If you think that you cannot factor the given equation, then you're right because there's no common factor at each terms. How about if you will expand the given equation and combine similar terms, then we can factor the resulting equation if possible? Let's expand the given equation, we have
Arrange the above equation according to their variables,
The last term, which is 3xyz can be written into three xyz's as follows
Group the above equation according to their variables, we have
Insert xyz at each group,
Remove their common factor at each group,
Since their common factor is (x - y + z), therefore, the factors of the given equation are
"Published in Newark, California, USA"
Find the factors for
Solution:
Consider the given equation above
If you think that you cannot factor the given equation, then you're right because there's no common factor at each terms. How about if you will expand the given equation and combine similar terms, then we can factor the resulting equation if possible? Let's expand the given equation, we have
Arrange the above equation according to their variables,
The last term, which is 3xyz can be written into three xyz's as follows
Group the above equation according to their variables, we have
Insert xyz at each group,
Remove their common factor at each group,
Since their common factor is (x - y + z), therefore, the factors of the given equation are
Thursday, November 7, 2013
Special Products - Factoring, 27
Category: Algebra
"Published in Newark, California, USA"
Find the factors for
Solution:
Consider the given equation above
Did you notice that the given equation is a quadratic equation of variables (x - 9b) and y? (x - 9b) is considered as a single variable. We have to do the trial and error method in getting the factors of (x - 9b)² and -2y² so that the middle term must be -(x - 9b)y. Let's start the factoring of the given equation as follows
The middle term is
Since the value of the above calculation is the same as the middle term of the given equation which is -y(x - 9b), then the factors of the given equation are
"Published in Newark, California, USA"
Find the factors for
Solution:
Consider the given equation above
Did you notice that the given equation is a quadratic equation of variables (x - 9b) and y? (x - 9b) is considered as a single variable. We have to do the trial and error method in getting the factors of (x - 9b)² and -2y² so that the middle term must be -(x - 9b)y. Let's start the factoring of the given equation as follows
The middle term is
Since the value of the above calculation is the same as the middle term of the given equation which is -y(x - 9b), then the factors of the given equation are
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