Graph P(x)=(x-5)(x-2)(x)

$P (x) = (x - 5) (x - 2) (x)$

Step 1

Find the point at $x = 1$ .

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

$f (1) = {(1)}^{3} - 7 {(1)}^{2} + 10 (1)$

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = 1 - 7 {(1)}^{2} + 10 (1)$

One to any power is one.

$f (1) = 1 - 7 \cdot 1 + 10 (1)$

Multiply $- 7$ by $1$ .

$f (1) = 1 - 7 + 10 (1)$

Multiply $10$ by $1$ .

$f (1) = 1 - 7 + 10$

Simplify by adding and subtracting.

Subtract $7$ from $1$ .

$f (1) = - 6 + 10$

Add $- 6$ and $10$ .

$f (1) = 4$

The final answer is $4$ .

$4$

Convert $4$ to decimal.

$y = 4$

Step 2

Find the point at $x = 2$ .

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

$f (2) = {(2)}^{3} - 7 {(2)}^{2} + 10 (2)$

Simplify the result.

Simplify each term.

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

$f (2) = 8 - 7 {(2)}^{2} + 10 (2)$

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

$f (2) = 8 - 7 \cdot 4 + 10 (2)$

Multiply $- 7$ by $4$ .

$f (2) = 8 - 28 + 10 (2)$

Multiply $10$ by $2$ .

$f (2) = 8 - 28 + 20$

Simplify by adding and subtracting.

Subtract $28$ from $8$ .

$f (2) = - 20 + 20$

Add $- 20$ and $20$ .

$f (2) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = 3$ .

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

$f (3) = {(3)}^{3} - 7 {(3)}^{2} + 10 (3)$

Simplify the result.

Simplify each term.

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

$f (3) = 27 - 7 {(3)}^{2} + 10 (3)$

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

$f (3) = 27 - 7 \cdot 9 + 10 (3)$

Multiply $- 7$ by $9$ .

$f (3) = 27 - 63 + 10 (3)$

Multiply $10$ by $3$ .

$f (3) = 27 - 63 + 30$

Simplify by adding and subtracting.

Subtract $63$ from $27$ .

$f (3) = - 36 + 30$

Add $- 36$ and $30$ .

$f (3) = - 6$

The final answer is $- 6$ .

$- 6$

Convert $- 6$ to decimal.

$y = - 6$

Step 4

Find the point at $x = 4$ .

Replace the variable $x$ with $4$ in the expression.

$f (4) = {(4)}^{3} - 7 {(4)}^{2} + 10 (4)$

Simplify the result.

Simplify each term.

Raise $4$ to the power of $3$ .

$f (4) = 64 - 7 {(4)}^{2} + 10 (4)$

Raise $4$ to the power of $2$ .

$f (4) = 64 - 7 \cdot 16 + 10 (4)$

Multiply $- 7$ by $16$ .

$f (4) = 64 - 112 + 10 (4)$

Multiply $10$ by $4$ .

$f (4) = 64 - 112 + 40$

Simplify by adding and subtracting.

Subtract $112$ from $64$ .

$f (4) = - 48 + 40$

Add $- 48$ and $40$ .

$f (4) = - 8$

The final answer is $- 8$ .

$- 8$

Convert $- 8$ to decimal.

$y = - 8$

Step 5

Find the point at $x = 5$ .

Replace the variable $x$ with $5$ in the expression.

$f (5) = {(5)}^{3} - 7 {(5)}^{2} + 10 (5)$

Simplify the result.

Simplify each term.

Raise $5$ to the power of $3$ .

$f (5) = 125 - 7 {(5)}^{2} + 10 (5)$

Raise $5$ to the power of $2$ .

$f (5) = 125 - 7 \cdot 25 + 10 (5)$

Multiply $- 7$ by $25$ .

$f (5) = 125 - 175 + 10 (5)$

Multiply $10$ by $5$ .

$f (5) = 125 - 175 + 50$

Simplify by adding and subtracting.

Subtract $175$ from $125$ .

$f (5) = - 50 + 50$

Add $- 50$ and $50$ .

$f (5) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 6

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

$\begin{array}{c} x & y \\ 1 & 4 \\ 2 & 0 \\ 3 & - 6 \\ 4 & - 8 \\ 5 & 0 \end{array}$

Step 7

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

Falls to the left and rises to the right

$\begin{array}{c} x & y \\ 1 & 4 \\ 2 & 0 \\ 3 & - 6 \\ 4 & - 8 \\ 5 & 0 \end{array}$

Step 8

Graph P(x)=(x-5)(x-2)(x)

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