Question

How do you solve `x^2+10x+9=0`?

Answer 1

To solve the trinomial we would need to factor this into two binomial factors and then set the two factors equal to zero.

`x^2+10x+9=0` can be factored into two binomials.

First list the factors of `x^2` x & x
now list the factors of 9, 1 & 9 and 3 & 3.

Place the factors of `x^2` as the first factors in the binomials.

(x ) (x ) = 0

Since the second sign of the trinomial is a (+) we know that we need to add the factors and the signs will be the same.

The factors of 9 that will add up to 10 are 1 & 9.
Since the first sign in the trinomial is a (+) we know that both signs will be positive.

(x + 9) (x + 1) = 0

Now set each of the binomials equal to zero, because if the binomial equals zero the product of the binomial solution will equal zero.

x + 9 = 0
x = -9

x + 1 = 0
x = -1

Since the highest exponent (degree) is 2 there will be two solutions.

x = -9 and x = -1

Here is a video on factoring trinomials.

SMARTERTEACHER YouTube