Algebra Examples

$y = {(x - 12)}^{3} - 10$

Step 1

Simplify each term.

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Step 1.1

Use the Binomial Theorem.

$y = x^{3} + 3 x^{2} \cdot - 12 + 3 x {(- 12)}^{2} + {(- 12)}^{3} - 10$

Step 1.2

Simplify each term.

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Step 1.2.1

Multiply $- 12$ by $3$ .

$y = x^{3} - 36 x^{2} + 3 x {(- 12)}^{2} + {(- 12)}^{3} - 10$

Step 1.2.2

Raise $- 12$ to the power of $2$ .

$y = x^{3} - 36 x^{2} + 3 x \cdot 144 + {(- 12)}^{3} - 10$

Step 1.2.3

Multiply $144$ by $3$ .

$y = x^{3} - 36 x^{2} + 432 x + {(- 12)}^{3} - 10$

Step 1.2.4

Raise $- 12$ to the power of $3$ .

$y = x^{3} - 36 x^{2} + 432 x - 1728 - 10$

Step 2

Subtract $10$ from $- 1728$ .

$y = x^{3} - 36 x^{2} + 432 x - 1738$

Step 3

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

$x^{3} \to 3$

$- 36 x^{2} \to 2$

$432 x \to 1$

$- 1738 \to 0$

Step 4

The largest exponent is the degree of the polynomial.

$3$

Step 5

The maximum number of possible roots is the degree of $x^{3} - 36 x^{2} + 432 x - 1738$ .

$3$