1) Combine like terms and simplify.

No further simplification is possible. The first term has a coefficient that can't be factored away. FOIL requires that all terms be multiplied by each other at some point, so the presence of the coefficient has to be reflected in every step of the factoring.

2) Practically speaking, that means we add an extra step. Multiply the coefficient of the first term by the last term before factoring.

3 * 6 = 18

Factors of 18 include:

1 + 18 = 19

2 + 9 = 11

3) Now pull out the common factor in each of the pairs, "3x" from the first two and "2" from the second two.

4) Pull out the "(x+3)" from both terms.

5) Set both parts equal to zero and solve.

3x + 2 = 0, x = –2/3

x + 3 = 0, x = –3

First, you need to factor the expression. This takes a little bit of trial and error, but even though the leading coefficient is not 1, there's only one way to get 2 (2 x 1) so that is helpful to remember!

Factored, the expression is .

Once you have those expressions, you can set them equal to 0 to get the roots, or solutions to the equation.

When you set .

And when you set

.

Those are your two roots!

You need to first factor the equation. Then you willbe able to set those expressions equal to 0 and find your roots. There is only one way to get your leading coefficient of 3 (3 x 1) so that's helpful when figuring it out.

In the form  remember you want a factor of  that when mulitplied by the factor of  and added together will give you the value of .

 Factored, it comes out to:

.

When you set those expressions equal to 0, you get

.

The roots of a quadratic can be found by factoring. Factoring the solution will give you an expression that when multiplying will result in the initial quadratic.

The roots for this expression are . Similarly the roots of a quadratic can be found using the quadratic quadratic formula where the parent function of a quadratic is represented as  and the quadratic formula is .

Roots when looking at a graph are simply the x-values of where the function crosses the x-axis.

Which, when looking at this graph, it is clearly

  and  

To solve this equation perform the oppisite operation to isolate the variable.

Recall that the square root of a negative number results in an imaginary number.

Therefore,

.

To solve this equation perform the oppisite operation to isolate the variable.

Recall that the square root of a negative number is an imaginary number.

Therefore,

.

The x-intercepts of a quadratic equation are also the solutions. To find them, factor the quadratic equation. After some trial and error, it can be factored to: . Set those expressions equal to  to get you x-intercepts. Your answers are: .

Find all solutions to the following quadratic equation:

We can solve the following equation by first bringing the -225 to the other side:

Next, take the square root of both sides.

Now, you may be tempted to write your answer as just

But, we need to remeber the following is also true

So our answer choice must include both positive and negative 15

To find the roots, or solutions, of the equation, factor the quadratic. It factors to . Then, set each expression equal to 0 to get your roots of 1 and 4.