MONOMIAL FACTORING
There are several forms of factoring in Algebra. We will focus on Monomial factoring on this page so that we can concentrate on a piece of Algebra's factoring. The photos provided tell us the mechanics of monomial factoring. Just study how the letter "a" colored in red, behaved. We will simply follow how its system works. Observed where is the letter "a" located. If you notice about "(ax + ay)", "a" is present in "x" and in "y" as well. Meaning, "a" is common to both "x and y" as property. We will remove their common and set it aside as you can see in "an (x + y)". The formula was fixed. You don't need to worry about it. It is the same monomial factoring in your early Algebra, you encountered if you did. Sometimes, the letter "a" can be changed to another character like the letter "b", "c", or mostly numbers. But the system works the same. If we just master the substitution, it would be fluent for you to do it easily.
Provided below were some examples as illustrations provided with answers. The common monomial was intentionally colored in red as extra assistance for monitoring the position of the common factor as to where it was located after the factoring. Please post your comment in the
"Post a comment " box is found at the bottom if there are questions.
Illustrative Examples for Common Monomial Factor:
Factor the following:
1. (c x + c y) = c (x + y)
Following the rules provided, x and y have the common letter "c", so "c" was set-asides and it was on the outside of the parenthesis like "c (x + y)".
2. (2 x - 2 y) = 2 (x - y)
In this case, "a" from the photos was changed into "2". Following the system of the formula, it gave us "2 (x + y)".. "x and y" have common which is "2".
3. (a m + a n) = a (m + n)
It's the same thing as our previous works. The "a" was common to "m and n". So we cast out "a" and now it was on the outside of "m and n" like "a (m + n)".
4. (5x P - 5x Q) = 5x (P - Q)
"5x" is common to "P and Q" in this example so 5x was cast out and by following the rules it gives us "5x (P - Q)".
5. (3 x + 6 y) = (3 x + 3*2 y) = 3 (x + 2y)
More examples with answers:
Factor the following:
1. (3 x - 3 y) = 3 (x - y)
2. (5 a + 5 b) = 5 (a + b)
3. (6 a - 2 b) = (3*2 a - 2 b) = 2 (3 a - b); (*) means multiply
4. (10 a + 8 b) = (5*2 a - 4*2 b) = 2 (5 a - 4 b)
5. 2 x + 4 y = 2*x + 2*2.y = 2( x + 2y); it's okay if there's no ( ) in the given problem, same rule applies
6. 6 a - 9 b = 2.3.a - 3.3.b = 3(2 a - 3 b)
7. 15 m + 9 n = 5*3 m+ 3*3 n = 3(5 m + 3 n)
8. 3 + 6 x = 3*1 + 3*2 x = 3 (1 + 2 x)
9. 12 a - 4 = 4*3 a - 4*1 = 4 (3 a - 1)
10). 2 a + 4 b - 6 c = 2.a + 2*2*b -2*3 c = 2(a + 2 b -3 c)
Show your result in the "Post a comment" box found at the bottom.
Factor:
Click the link below to:
Provided below were some examples as illustrations provided with answers. The common monomial was intentionally colored in red as extra assistance for monitoring the position of the common factor as to where it was located after the factoring. Please post your comment in the
"Post a comment " box is found at the bottom if there are questions.
Illustrative Examples for Common Monomial Factor:
Factor the following:
1. (c x + c y) = c (x + y)
Following the rules provided, x and y have the common letter "c", so "c" was set-asides and it was on the outside of the parenthesis like "c (x + y)".
2. (2 x - 2 y) = 2 (x - y)
In this case, "a" from the photos was changed into "2". Following the system of the formula, it gave us "2 (x + y)".. "x and y" have common which is "2".
3. (a m + a n) = a (m + n)
It's the same thing as our previous works. The "a" was common to "m and n". So we cast out "a" and now it was on the outside of "m and n" like "a (m + n)".
4. (5x P - 5x Q) = 5x (P - Q)
"5x" is common to "P and Q" in this example so 5x was cast out and by following the rules it gives us "5x (P - Q)".
5. (3 x + 6 y) = (3 x + 3*2 y) = 3 (x + 2y)
This example, it shows a little bit tricky. but in the "(3 x + 6 y)", 6 was factored in to "3x2" so the new scene can be "(3 x + 3x2 y)", which shows "3" is common. Following the rules provided will result in " 3( x + 2 y)".
More examples with answers:
Factor the following:
1. (3 x - 3 y) = 3 (x - y)
2. (5 a + 5 b) = 5 (a + b)
3. (6 a - 2 b) = (3*2 a - 2 b) = 2 (3 a - b); (*) means multiply
4. (10 a + 8 b) = (5*2 a - 4*2 b) = 2 (5 a - 4 b)
5. 2 x + 4 y = 2*x + 2*2.y = 2( x + 2y); it's okay if there's no ( ) in the given problem, same rule applies
6. 6 a - 9 b = 2.3.a - 3.3.b = 3(2 a - 3 b)
7. 15 m + 9 n = 5*3 m+ 3*3 n = 3(5 m + 3 n)
8. 3 + 6 x = 3*1 + 3*2 x = 3 (1 + 2 x)
9. 12 a - 4 = 4*3 a - 4*1 = 4 (3 a - 1)
10). 2 a + 4 b - 6 c = 2.a + 2*2*b -2*3 c = 2(a + 2 b -3 c)
Try these yourself:
Show your result in the "Post a comment" box found at the bottom.
Factor:
Click the link below to:
Home
