Write as a Set of Linear Factors x^3-18x-8=0

$x^{3} - 18 x - 8 = 0$

If a polynomial function has integer coefficients, then every rational zero will have the form $\frac{p}{q}$ where $p$ is a factor of the constant and $q$ is a factor of the leading coefficient.

$p = \pm 1, \pm 8, \pm 2, \pm 4$

$q = \pm 1 = 0$

Find every combination of $\pm \frac{p}{q}$ . These are the possible roots of the polynomial function.

$\pm 1, \pm 8, \pm 2, \pm 4 = 0$

Substitute $- 4$ and simplify the expression. In this case, the expression is equal to $0$ so $- 4$ is a root of the polynomial.

Substitute $- 4$ into the polynomial.

${(- 4)}^{3} - 18 \cdot - 4 - 8 = 0$

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

$- 64 - 18 \cdot - 4 - 8 = 0$

Multiply $- 18$ by $- 4$ .

$- 64 + 72 - 8 = 0$

Add $- 64$ and $72$ .

$8 - 8 = 0$

Subtract $8$ from $8$ .

$0 = 0$

Since $- 4$ is a known root, divide the polynomial by $x + 4$ to find the quotient polynomial. This polynomial can then be used to find the remaining roots.

$\frac{x^{3} - 18 x - 8}{x + 4} = 0$

Divide $x^{3} - 18 x - 8$ by $x + 4$ .

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of $0$ .

$= 0$

Divide the highest order term in the dividend $x^{3}$ by the highest order term in divisor $x$ .

$= 0$

Multiply the new quotient term by the divisor.

$= 0$

The expression needs to be subtracted from the dividend, so change all the signs in $x^{3} + 4 x^{2}$

$= 0$

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

$= 0$

Pull the next terms from the original dividend down into the current dividend.

$= 0$

Divide the highest order term in the dividend $- 4 x^{2}$ by the highest order term in divisor $x$ .

$= 0$

Multiply the new quotient term by the divisor.

$= 0$

The expression needs to be subtracted from the dividend, so change all the signs in $- 4 x^{2} - 16 x$

$= 0$

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

$= 0$

Pull the next terms from the original dividend down into the current dividend.

$= 0$

Divide the highest order term in the dividend $- 2 x$ by the highest order term in divisor $x$ .

$= 0$

Multiply the new quotient term by the divisor.

$= 0$

The expression needs to be subtracted from the dividend, so change all the signs in $- 2 x - 8$

$= 0$

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

$= 0$

Since the remander is $0$ , the final answer is the quotient.

$x^{2} - 4 x - 2 = 0$

Write $x^{3} - 18 x - 8$ as a set of factors.

$(x + 4) (x^{2} - 4 x - 2) = 0$

Write as a Set of Linear Factors x^3-18x-8=0

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