Find the x and y Intercepts (x^2-4x+3)/(x+1)

$\frac{x^{2} - 4 x + 3}{x + 1}$

Step 1

Write $\frac{x^{2} - 4 x + 3}{x + 1}$ as an equation.

$y = \frac{x^{2} - 4 x + 3}{x + 1}$

Step 2

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \frac{x^{2} - 4 x + 3}{x + 1}$

Solve the equation.

Set the numerator equal to zero.

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

Solve the equation for $x$ .

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

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 $- 4$ .

$- 3, - 1$

Write the factored form using these integers.

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

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

$x - 3 = 0$

$x - 1 = 0$

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

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

$x - 3 = 0$

Add $3$ to both sides of the equation.

$x = 3$

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

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

$x - 1 = 0$

Add $1$ to both sides of the equation.

$x = 1$

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

$x = 3, 1$

x-intercept(s) in point form.

x-intercept(s): $(3, 0), (1, 0)$

Step 3

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \frac{{(0)}^{2} - 4 \cdot 0 + 3}{(0) + 1}$

Solve the equation.

Remove parentheses.

$y = \frac{0^{2} - 4 \cdot 0 + 3}{(0) + 1}$

Remove parentheses.

$y = \frac{0^{2} - 4 \cdot 0 + 3}{0 + 1}$

Remove parentheses.

$y = \frac{{(0)}^{2} - 4 \cdot 0 + 3}{(0) + 1}$

Simplify $\frac{{(0)}^{2} - 4 \cdot 0 + 3}{(0) + 1}$ .

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$y = \frac{0 - 4 \cdot 0 + 3}{0 + 1}$

Multiply $- 4$ by $0$ .

$y = \frac{0 + 0 + 3}{0 + 1}$

Add $0$ and $0$ .

$y = \frac{0 + 3}{0 + 1}$

Add $0$ and $3$ .

$y = \frac{3}{0 + 1}$

Simplify the expression.

Add $0$ and $1$ .

$y = \frac{3}{1}$

Divide $3$ by $1$ .

$y = 3$

y-intercept(s) in point form.

y-intercept(s): $(0, 3)$

Step 4

List the intersections.

x-intercept(s): $(3, 0), (1, 0)$

y-intercept(s): $(0, 3)$

Step 5

Find the x and y Intercepts (x^2-4x+3)/(x+1)

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