Trigonometry Examples

$f (x) = x^{2} + 4 x + 3$

Step 1

Set $x^{2} + 4 x + 3$ equal to $0$ .

$x^{2} + 4 x + 3 = 0$

Step 2

Solve for $x$ .

Tap for more steps...

Step 2.1

Factor $x^{2} + 4 x + 3$ using the AC method.

Tap for more steps...

Step 2.1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $3$ and whose sum is $4$ .

$1, 3$

Step 2.1.2

Write the factored form using these integers.

$(x + 1) (x + 3) = 0$

Step 2.2

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x + 1 = 0$

$x + 3 = 0$

Step 2.3

Set $x + 1$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 2.3.1

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Step 2.3.2

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 2.4

Set $x + 3$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 2.4.1

Set $x + 3$ equal to $0$ .

$x + 3 = 0$

Step 2.4.2

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 2.5

The final solution is all the values that make $(x + 1) (x + 3) = 0$ true.

$x = - 1, - 3$

Step 3