so factor it out:5x(7y-12x)-Look. Factoring = Taking out the common things.Look at each term in the first example:6* (x^3) + 18* (x^2)Now remember this: This is very important: x^3 = (x^2) * xso we have:6 * (x^2) * x + 18 * (x^2)What is common in these two terms? It is the (x^2) part. Take it out and write:(x^2) ( 6*x + 18)now what else is common here? Again remember: 6 * 3 = 18so you have: (x^2) ( 6*x + 6*3)so you take the 6 out again:6 * (x^2) ( x + 3 )That is your answer.......
3(m^2 +8m +12)
Then figure out how you can split that up to make the numbers work out. Looking at the first and last digits, you'll see that the form will be (m+_)(m+_). Then just start putting numbers in that will equal 12 when multiplied, but will also satisfy the 8m part when the outer and inner terms of the FOIL method are added together. You come up with:
3(m+6)(m+2)
Final example:
35xy -60x^2
5x is common to both, so factor it out:
5x(7y-12x)
Look. Factoring = Taking out the common things.
Look at each term in the first example:
6* (x^3) + 18* (x^2)
Now remember this: This is very important: x^3 = (x^2) * x
so we have:
6 * (x^2) * x + 18 * (x^2)
What is common in these two terms? It is the (x^2) part. Take it out and write:
(x^2) ( 6*x + 18)
now what else is common here? Again remember: 6 * 3 = 18
so you have:
(x^2) ( 6*x + 6*3)
so you take the 6 out again:
6 * (x^2) ( x + 3 )
That is your answer.
