Graph P(x)=x(2x+5)(x+1)

$P (x) = x (2 x + 5) (x + 1)$

Step 1

Find the point at $x = - 3$ .

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

$f (- 3) = 2 {(- 3)}^{3} + 7 {(- 3)}^{2} + 5 (- 3)$

Simplify the result.

Simplify each term.

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

$f (- 3) = 2 \cdot - 27 + 7 {(- 3)}^{2} + 5 (- 3)$

Multiply $2$ by $- 27$ .

$f (- 3) = - 54 + 7 {(- 3)}^{2} + 5 (- 3)$

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

$f (- 3) = - 54 + 7 \cdot 9 + 5 (- 3)$

Multiply $7$ by $9$ .

$f (- 3) = - 54 + 63 + 5 (- 3)$

Multiply $5$ by $- 3$ .

$f (- 3) = - 54 + 63 - 15$

Simplify by adding and subtracting.

Add $- 54$ and $63$ .

$f (- 3) = 9 - 15$

Subtract $15$ from $9$ .

$f (- 3) = - 6$

The final answer is $- 6$ .

$- 6$

Convert $- 6$ to decimal.

$y = - 6$

Step 2

Find the point at $x = - 2$ .

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

$f (- 2) = 2 {(- 2)}^{3} + 7 {(- 2)}^{2} + 5 (- 2)$

Simplify the result.

Simplify each term.

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

$f (- 2) = 2 \cdot - 8 + 7 {(- 2)}^{2} + 5 (- 2)$

Multiply $2$ by $- 8$ .

$f (- 2) = - 16 + 7 {(- 2)}^{2} + 5 (- 2)$

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

$f (- 2) = - 16 + 7 \cdot 4 + 5 (- 2)$

Multiply $7$ by $4$ .

$f (- 2) = - 16 + 28 + 5 (- 2)$

Multiply $5$ by $- 2$ .

$f (- 2) = - 16 + 28 - 10$

Simplify by adding and subtracting.

Add $- 16$ and $28$ .

$f (- 2) = 12 - 10$

Subtract $10$ from $12$ .

$f (- 2) = 2$

The final answer is $2$ .

$2$

Convert $2$ to decimal.

$y = 2$

Step 3

Find the point at $x = - 1$ .

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

$f (- 1) = 2 {(- 1)}^{3} + 7 {(- 1)}^{2} + 5 (- 1)$

Simplify the result.

Simplify each term.

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

$f (- 1) = 2 \cdot - 1 + 7 {(- 1)}^{2} + 5 (- 1)$

Multiply $2$ by $- 1$ .

$f (- 1) = - 2 + 7 {(- 1)}^{2} + 5 (- 1)$

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

$f (- 1) = - 2 + 7 \cdot 1 + 5 (- 1)$

Multiply $7$ by $1$ .

$f (- 1) = - 2 + 7 + 5 (- 1)$

Multiply $5$ by $- 1$ .

$f (- 1) = - 2 + 7 - 5$

Simplify by adding and subtracting.

Add $- 2$ and $7$ .

$f (- 1) = 5 - 5$

Subtract $5$ from $5$ .

$f (- 1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 4

Find the point at $x = 1$ .

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

$f (1) = 2 {(1)}^{3} + 7 {(1)}^{2} + 5 (1)$

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = 2 \cdot 1 + 7 {(1)}^{2} + 5 (1)$

Multiply $2$ by $1$ .

$f (1) = 2 + 7 {(1)}^{2} + 5 (1)$

One to any power is one.

$f (1) = 2 + 7 \cdot 1 + 5 (1)$

Multiply $7$ by $1$ .

$f (1) = 2 + 7 + 5 (1)$

Multiply $5$ by $1$ .

$f (1) = 2 + 7 + 5$

Simplify by adding numbers.

Add $2$ and $7$ .

$f (1) = 9 + 5$

Add $9$ and $5$ .

$f (1) = 14$

The final answer is $14$ .

$14$

Convert $14$ to decimal.

$y = 14$

Step 5

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

$\begin{array}{c} x & y \\ - 3 & - 6 \\ - 2 & 2 \\ - 1 & 0 \\ 0 & 0 \\ 1 & 14 \end{array}$

Step 6

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

Falls to the left and rises to the right

$\begin{array}{c} x & y \\ - 3 & - 6 \\ - 2 & 2 \\ - 1 & 0 \\ 0 & 0 \\ 1 & 14 \end{array}$

Step 7

Graph P(x)=x(2x+5)(x+1)

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