- foiling (or factoring), which is what TPH demonstrated earlier
- completing the square
- the quadratic formula
When we want to foil we have to come up with two numbers. these numbers must be such that when we multiply them together we get the constant term (we must account for the sign), and when we add them together we get the coefficient of (we must also account for the sign). So as you see, here we must come up with two numbers that when multiplied we get +6 and when added, we get +7. it is simple enough to come up with such numbers, and since TPH did the problem already, it would be no surprise that these numbers are +1 and +6. since (+1)*(+6) = +6 our lone constant, and +1 + 6 = + 7 our coefficient of
once we have these two numbers, we simply foil the expression putting them in two sets of brackets with 's in front of them. so we get:
now if two numbers when multiplied gives a result of zero, it means one or the other is zero. so then:
How do we know when to use the above method and when to use the quadratic formula? Simple. If you can't come up with two numbers, use the formula.
Now to refresh your memory, the quadratic formula is given and explained below.
Given a quadratic of the form:
The roots of the quadratic (that is the -values that make the quadratic = 0) are given by the formula:
Now, try the others
completing the square, quadratic formula, factoring
You want to try to use factoring first. It's much easier. If you have a quadratic ( ) with an of 1, you want to look to use factoring. If it don't work, use complete the square/quadratic formula. If is any real number besides 1 or 0, you want to look to use the "ac" method, which is a variation of factoring. If it don't work, use the quadratic formula/complete the square.
Do you all agree with this?
This is my 21th post!!!!!!!
So if I were to solve this problem 6n^2 + 7n = 20 would it be
6n^2 + 7n + 20 and then multiply 6 & 20 and then find the 2 numbers of 120 that will add to positive seven. Then once I find the 2 numbers, do the grouping part. I think I might be confusing you? Thanks for the help with the other problem