Find the x and y Intercepts f(x)=(x+2)(x-1)(x-(4+3i))(x-(4-3i))

$f (x) = (x + 2) (x - 1) (x - (4 + 3 i)) (x - (4 - 3 i))$

Find the x-intercepts.

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

$0 = (x + 2) (x - 1) (x - (4 + 3 i)) (x - (4 - 3 i))$

Solve the equation.

Rewrite the equation as $(x + 2) (x - 1) (x - (4 + 3 i)) (x - (4 - 3 i)) = 0$ .

$(x + 2) (x - 1) (x - (4 + 3 i)) (x - (4 - 3 i)) = 0$

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

$x + 2 = 0$

$x - 1 = 0$

$x - (4 + 3 i) = 0$

$x - (4 - 3 i) = 0$

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

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.

$x = 1$

Set $x - (4 + 3 i)$ equal to $0$ and solve for $x$ .

Set $x - (4 + 3 i)$ equal to $0$ .

$x - (4 + 3 i) = 0$

Solve $x - (4 + 3 i) = 0$ for $x$ .

Simplify each term.

Apply the distributive property.

$x - 1 \cdot 4 - (3 i) = 0$

Multiply $- 1$ by $4$ .

$x - 4 - (3 i) = 0$

Multiply $3$ by $- 1$ .

$x - 4 - 3 i = 0$

Move all terms not containing $x$ to the right side of the equation.

Add $4$ to both sides of the equation.

$x - 3 i = 4$

Add $3 i$ to both sides of the equation.

$x = 4 + 3 i$

Set $x - (4 - 3 i)$ equal to $0$ and solve for $x$ .

Set $x - (4 - 3 i)$ equal to $0$ .

$x - (4 - 3 i) = 0$

Solve $x - (4 - 3 i) = 0$ for $x$ .

Simplify each term.

Apply the distributive property.

$x - 1 \cdot 4 - (- 3 i) = 0$

Multiply $- 1$ by $4$ .

$x - 4 - (- 3 i) = 0$

Multiply $- 3$ by $- 1$ .

$x - 4 + 3 i = 0$

Move all terms not containing $x$ to the right side of the equation.

Add $4$ to both sides of the equation.

$x + 3 i = 4$

Subtract $3 i$ from both sides of the equation.

$x = 4 - 3 i$

The final solution is all the values that make $(x + 2) (x - 1) (x - (4 + 3 i)) (x - (4 - 3 i)) = 0$ true.

$x = - 2, 1, 4 + 3 i, 4 - 3 i$

x-intercept(s) in point form.

x-intercept(s): $(- 2, 0), (1, 0)$

Find the y-intercepts.

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

$y = ((0) + 2) ((0) - 1) ((0) - (4 + 3 i)) ((0) - (4 - 3 i))$

Solve the equation.

Remove parentheses.

$y = (0 + 2) ((0) - 1) ((0) - (4 + 3 i)) ((0) - (4 - 3 i))$

Remove parentheses.

$y = (0 + 2) (0 - 1) ((0) - (4 + 3 i)) ((0) - (4 - 3 i))$

Remove parentheses.

$y = (0 + 2) (0 - 1) (0 - (4 + 3 i)) ((0) - (4 - 3 i))$

Remove parentheses.

$y = (0 + 2) (0 - 1) (0 - (4 + 3 i)) (0 - (4 - 3 i))$

Remove parentheses.

$y = ((0) + 2) ((0) - 1) ((0) - (4 + 3 i)) ((0) - (4 - 3 i))$

Simplify $((0) + 2) ((0) - 1) ((0) - (4 + 3 i)) ((0) - (4 - 3 i))$ .

Simplify terms.

Add $0$ and $2$ .

$y = 2 ((0) - 1) ((0) - (4 + 3 i)) ((0) - (4 - 3 i))$

Simplify the expression.

Subtract $1$ from $0$ .

$y = 2 \cdot - 1 ((0) - (4 + 3 i)) ((0) - (4 - 3 i))$

Multiply $2$ by $- 1$ .

$y = - 2 ((0) - (4 + 3 i)) ((0) - (4 - 3 i))$

Simplify each term.

Apply the distributive property.

$y = - 2 (0 - 1 \cdot 4 - (3 i)) ((0) - (4 - 3 i))$

Multiply $- 1$ by $4$ .

$y = - 2 (0 - 4 - (3 i)) ((0) - (4 - 3 i))$

Multiply $3$ by $- 1$ .

$y = - 2 (0 - 4 - 3 i) ((0) - (4 - 3 i))$

Simplify by multiplying through.

Subtract $4$ from $0$ .

$y = - 2 (- 4 - 3 i) ((0) - (4 - 3 i))$

Apply the distributive property.

$y = (- 2 \cdot - 4 - 2 (- 3 i)) ((0) - (4 - 3 i))$

Multiply.

Multiply $- 2$ by $- 4$ .

$y = (8 - 2 (- 3 i)) ((0) - (4 - 3 i))$

Multiply $- 3$ by $- 2$ .

$y = (8 + 6 i) ((0) - (4 - 3 i))$

Simplify each term.

Apply the distributive property.

$y = (8 + 6 i) (0 - 1 \cdot 4 - (- 3 i))$

Multiply $- 1$ by $4$ .

$y = (8 + 6 i) (0 - 4 - (- 3 i))$

Multiply $- 3$ by $- 1$ .

$y = (8 + 6 i) (0 - 4 + 3 i)$

Subtract $4$ from $0$ .

$y = (8 + 6 i) (- 4 + 3 i)$

Expand $(8 + 6 i) (- 4 + 3 i)$ using the FOIL Method.

Apply the distributive property.

$y = 8 (- 4 + 3 i) + 6 i (- 4 + 3 i)$

Apply the distributive property.

$y = 8 \cdot - 4 + 8 (3 i) + 6 i (- 4 + 3 i)$

Apply the distributive property.

$y = 8 \cdot - 4 + 8 (3 i) + 6 i \cdot - 4 + 6 i (3 i)$

Simplify and combine like terms.

Simplify each term.

Multiply $8$ by $- 4$ .

$y = - 32 + 8 (3 i) + 6 i \cdot - 4 + 6 i (3 i)$

Multiply $3$ by $8$ .

$y = - 32 + 24 i + 6 i \cdot - 4 + 6 i (3 i)$

Multiply $- 4$ by $6$ .

$y = - 32 + 24 i - 24 i + 6 i (3 i)$

Multiply $6 i (3 i)$ .

Multiply $3$ by $6$ .

$y = - 32 + 24 i - 24 i + 18 i i$

Raise $i$ to the power of $1$ .

$y = - 32 + 24 i - 24 i + 18 (i^{1} i)$

Raise $i$ to the power of $1$ .

$y = - 32 + 24 i - 24 i + 18 (i^{1} i^{1})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = - 32 + 24 i - 24 i + 18 i^{1 + 1}$

Add $1$ and $1$ .

$y = - 32 + 24 i - 24 i + 18 i^{2}$

Rewrite $i^{2}$ as $- 1$ .

$y = - 32 + 24 i - 24 i + 18 \cdot - 1$

Multiply $18$ by $- 1$ .

$y = - 32 + 24 i - 24 i - 18$

Subtract $18$ from $- 32$ .

$y = - 50 + 24 i - 24 i$

Subtract $24 i$ from $24 i$ .

$y = - 50 + 0$

Add $- 50$ and $0$ .

$y = - 50$

y-intercept(s) in point form.

y-intercept(s): $(0, - 50)$

List the intersections.

x-intercept(s): $(- 2, 0), (1, 0)$

y-intercept(s): $(0, - 50)$

Find the x and y Intercepts f(x)=(x+2)(x-1)(x-(4+3i))(x-(4-3i))

Related Questions

Support LCMGCF.com by disabling your adblocker.