how do u solve x²+5x+6=?

Question

x^²+ 5x+6 

Answer 1

You're looking to factor the quadratic. I'm going to assume that 0 is on the right hand side. If it isn't 0, you'll have to get 0 on the other side by adding/subtracting as necessary. 

 

Once you have x²+5x+6 = 0, you have a few options. The easiest way (but the way that will require the most insight and practice) is the following:

 

Because the coefficient on the x² is 1, you know that both parts of the factor will have a plain x:

 

(x ± ?)(x ± ?)

 

When you factor this way, you will look for two numbers (that will go where the question marks are) that do two things. First, they must multiply together to get the term that doesn't have an x, which in this case is 6. Second, they must add together to give you the coefficient attached to x, which in this case is 5. 

 

So we do a little guess and check. This is where the practice comes in. Because 5x and 6 are both positive, both numbers are positive. How do we know? There isn't any way to add two negative numbers and get +5 and there isn't any way to multiple a positive and negative number to get +6. So now we know it must be like this:

(x + ?)(x + ?)

 

Next, we think of two positive numbers that when added together give 5 but when multiplied together give 6. Let's try 2 and 3. 2+3 = 5 and 2*3 = 6. So those are our numbers. 

 

(x+2)(x+3)

 

You can check this by multiplying them together (You probably know this by the FOIL method). When you do, you get the following:

x²+5x+6

 

We know that our numbers are correct. 

 

Remember, These two factors are set equal to 0, so we can solve for x. 

 

(x+2)(x+3) = 0

 

Because you can multiply them together to get 0, one or both must be zero. Using this, we can set one equal to 0 and solve for the other.

 

(x+2) = 0; x = -2

(x+3) = 0; x = -3

 

Hope this helps!

(x ± ?)
(x ± ?)
(x ± ?)