Identify the Zeros and Their Multiplicities y=2(x+5)^3+10

$y = 2 {(x + 5)}^{3} + 10$

Step 1

Set $2 {(x + 5)}^{3} + 10$ equal to $0$ .

$2 {(x + 5)}^{3} + 10 = 0$

Step 2

Solve for $x$ .

Simplify $2 {(x + 5)}^{3} + 10$ .

Simplify each term.

Use the Binomial Theorem.

$2 (x^{3} + 3 x^{2} \cdot 5 + 3 x \cdot 5^{2} + 5^{3}) + 10 = 0$

Simplify each term.

Multiply $5$ by $3$ .

$2 (x^{3} + 15 x^{2} + 3 x \cdot 5^{2} + 5^{3}) + 10 = 0$

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

$2 (x^{3} + 15 x^{2} + 3 x \cdot 25 + 5^{3}) + 10 = 0$

Multiply $25$ by $3$ .

$2 (x^{3} + 15 x^{2} + 75 x + 5^{3}) + 10 = 0$

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

$2 (x^{3} + 15 x^{2} + 75 x + 125) + 10 = 0$

Apply the distributive property.

$2 x^{3} + 2 (15 x^{2}) + 2 (75 x) + 2 \cdot 125 + 10 = 0$

Simplify.

Multiply $15$ by $2$ .

$2 x^{3} + 30 x^{2} + 2 (75 x) + 2 \cdot 125 + 10 = 0$

Multiply $75$ by $2$ .

$2 x^{3} + 30 x^{2} + 150 x + 2 \cdot 125 + 10 = 0$

Multiply $2$ by $125$ .

$2 x^{3} + 30 x^{2} + 150 x + 250 + 10 = 0$

Add $250$ and $10$ .

$2 x^{3} + 30 x^{2} + 150 x + 260 = 0$

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 6.70997594$ (Multiplicity of $1$ )

Step 3