Graph p(x)=(x+5)(2x+3)(x-2)

$p (x) = (x + 5) (2 x + 3) (x - 2)$

Find the point at $x = - 3$ .

Replace the variable $x$ with $- 3$ in the expression.

$f (- 3) = 2 {(- 3)}^{3} + 9 {(- 3)}^{2} - 11 \cdot - 3 - 30$

Simplify the result.

Simplify each term.

Raise $- 3$ to the power of $3$ .

$f (- 3) = 2 \cdot - 27 + 9 {(- 3)}^{2} - 11 \cdot - 3 - 30$

Multiply $2$ by $- 27$ .

$f (- 3) = - 54 + 9 {(- 3)}^{2} - 11 \cdot - 3 - 30$

Raise $- 3$ to the power of $2$ .

$f (- 3) = - 54 + 9 \cdot 9 - 11 \cdot - 3 - 30$

Multiply $9$ by $9$ .

$f (- 3) = - 54 + 81 - 11 \cdot - 3 - 30$

Multiply $- 11$ by $- 3$ .

$f (- 3) = - 54 + 81 + 33 - 30$

Simplify by adding and subtracting.

Add $- 54$ and $81$ .

$f (- 3) = 27 + 33 - 30$

Add $27$ and $33$ .

$f (- 3) = 60 - 30$

Subtract $30$ from $60$ .

$f (- 3) = 30$

The final answer is $30$ .

$30$

Convert $30$ to decimal.

$y = 30$

Find the point at $x = - 2$ .

Replace the variable $x$ with $- 2$ in the expression.

$f (- 2) = 2 {(- 2)}^{3} + 9 {(- 2)}^{2} - 11 \cdot - 2 - 30$

Simplify the result.

Simplify each term.

Raise $- 2$ to the power of $3$ .

$f (- 2) = 2 \cdot - 8 + 9 {(- 2)}^{2} - 11 \cdot - 2 - 30$

Multiply $2$ by $- 8$ .

$f (- 2) = - 16 + 9 {(- 2)}^{2} - 11 \cdot - 2 - 30$

Raise $- 2$ to the power of $2$ .

$f (- 2) = - 16 + 9 \cdot 4 - 11 \cdot - 2 - 30$

Multiply $9$ by $4$ .

$f (- 2) = - 16 + 36 - 11 \cdot - 2 - 30$

Multiply $- 11$ by $- 2$ .

$f (- 2) = - 16 + 36 + 22 - 30$

Simplify by adding and subtracting.

Add $- 16$ and $36$ .

$f (- 2) = 20 + 22 - 30$

Add $20$ and $22$ .

$f (- 2) = 42 - 30$

Subtract $30$ from $42$ .

$f (- 2) = 12$

The final answer is $12$ .

$12$

Convert $12$ to decimal.

$y = 12$

Find the point at $x = - 1$ .

Replace the variable $x$ with $- 1$ in the expression.

$f (- 1) = 2 {(- 1)}^{3} + 9 {(- 1)}^{2} - 11 \cdot - 1 - 30$

Simplify the result.

Simplify each term.

Raise $- 1$ to the power of $3$ .

$f (- 1) = 2 \cdot - 1 + 9 {(- 1)}^{2} - 11 \cdot - 1 - 30$

Multiply $2$ by $- 1$ .

$f (- 1) = - 2 + 9 {(- 1)}^{2} - 11 \cdot - 1 - 30$

Raise $- 1$ to the power of $2$ .

$f (- 1) = - 2 + 9 \cdot 1 - 11 \cdot - 1 - 30$

Multiply $9$ by $1$ .

$f (- 1) = - 2 + 9 - 11 \cdot - 1 - 30$

Multiply $- 11$ by $- 1$ .

$f (- 1) = - 2 + 9 + 11 - 30$

Simplify by adding and subtracting.

Add $- 2$ and $9$ .

$f (- 1) = 7 + 11 - 30$

Add $7$ and $11$ .

$f (- 1) = 18 - 30$

Subtract $30$ from $18$ .

$f (- 1) = - 12$

The final answer is $- 12$ .

$- 12$

Convert $- 12$ to decimal.

$y = - 12$

Find the point at $x = 0$ .

Replace the variable $x$ with $0$ in the expression.

$f (0) = 2 {(0)}^{3} + 9 {(0)}^{2} - 11 \cdot 0 - 30$

Simplify the result.

Simplify each term.

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

$f (0) = 2 \cdot 0 + 9 {(0)}^{2} - 11 \cdot 0 - 30$

Multiply $2$ by $0$ .

$f (0) = 0 + 9 {(0)}^{2} - 11 \cdot 0 - 30$

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

$f (0) = 0 + 9 \cdot 0 - 11 \cdot 0 - 30$

Multiply $9$ by $0$ .

$f (0) = 0 + 0 - 11 \cdot 0 - 30$

Multiply $- 11$ by $0$ .

$f (0) = 0 + 0 + 0 - 30$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$f (0) = 0 + 0 - 30$

Add $0$ and $0$ .

$f (0) = 0 - 30$

Subtract $30$ from $0$ .

$f (0) = - 30$

The final answer is $- 30$ .

$- 30$

Convert $- 30$ to decimal.

$y = - 30$

The cubic function can be graphed using the function behavior and the points.

$\begin{array}{c} x & y \\ - 3 & 30 \\ - 2 & 12 \\ - 1 & - 12 \\ 0 & - 30 \\ 1 & - 30 \end{array}$

The cubic function can be graphed using the function behavior and the selected points.

Falls to the left and rises to the right

$\begin{array}{c} x & y \\ - 3 & 30 \\ - 2 & 12 \\ - 1 & - 12 \\ 0 & - 30 \\ 1 & - 30 \end{array}$

Graph p(x)=(x+5)(2x+3)(x-2)

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