Factoring the following quadratic:
(10 Points)
x^2 + 9x + 14

(x + 2)(x + 7)

Step-by-step explanation:

To factor a quadratic equation you have to figure out what factors of 14 equal 9 when they are combined. To do this, let's first find all of the factors of 14.

1 * 14 = 14

1 and 14 don't work because 1 + 14 9 and -14 + (-1) 9

2 * 7 = 14

This works because 2 + 7 = 9.

Now we can move on to factoring the equation.

Both of the xs are positive because the x in the quadratic form has a positive coefficient.

The 2 and the 7 are also both positive because the 9 is positive.

So, we end up getting:

(x + 2) (x + 7)

We can check to make sure this is correct by turning it back into a quadratic equation:

x * x = x^2

x * 7 = 7x

x * 2 = 2x

2 * 7 = 14

x^2 + 7x + 2x + 14

Combine like terms, and you get the original quadratic equation:

x^2 + 9x + 14

Hope this helps!

; )

step-by-step explanation: ; )