Write as a Set of Linear Factors g(x)=x^3-4x^2-5x+14

$g (x) = x^{3} - 4 x^{2} - 5 x + 14$

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.

$g (x) = p = \pm 1, \pm 14, \pm 2, \pm 7$

$q = \pm 1$

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

$g (x) = \pm 1, \pm 14, \pm 2, \pm 7$

Substitute $- 2$ and simplify the expression. In this case, the expression is equal to $0$ so $- 2$ is a root of the polynomial.

Substitute $- 2$ into the polynomial.

$g (x) = {(- 2)}^{3} - 4 {(- 2)}^{2} - 5 \cdot - 2 + 14$

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

$g (x) = - 8 - 4 {(- 2)}^{2} - 5 \cdot - 2 + 14$

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

$g (x) = - 8 - 4 \cdot 4 - 5 \cdot - 2 + 14$

Multiply $- 4$ by $4$ .

$g (x) = - 8 - 16 - 5 \cdot - 2 + 14$

Subtract $16$ from $- 8$ .

$g (x) = - 24 - 5 \cdot - 2 + 14$

Multiply $- 5$ by $- 2$ .

$g (x) = - 24 + 10 + 14$

Add $- 24$ and $10$ .

$g (x) = - 14 + 14$

Add $- 14$ and $14$ .

$g (x) = 0$

Since $- 2$ is a known root, divide the polynomial by $x + 2$ to find the quotient polynomial. This polynomial can then be used to find the remaining roots.

$g (x) = \frac{x^{3} - 4 x^{2} - 5 x + 14}{x + 2}$

Divide $x^{3} - 4 x^{2} - 5 x + 14$ by $x + 2$ .

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

$g (x) =$

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

$g (x) =$

Multiply the new quotient term by the divisor.

$g (x) =$

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

$g (x) =$

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

$g (x) =$

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

$g (x) =$

Divide the highest order term in the dividend $- 6 x^{2}$ by the highest order term in divisor $x$ .

$g (x) =$

Multiply the new quotient term by the divisor.

$g (x) =$

The expression needs to be subtracted from the dividend, so change all the signs in $- 6 x^{2} - 12 x$

$g (x) =$

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

$g (x) =$

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

$g (x) =$

Divide the highest order term in the dividend $7 x$ by the highest order term in divisor $x$ .

$g (x) =$

Multiply the new quotient term by the divisor.

$g (x) =$

The expression needs to be subtracted from the dividend, so change all the signs in $7 x + 14$

$g (x) =$

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

$g (x) =$

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

$g (x) = x^{2} - 6 x + 7$

Write $x^{3} - 4 x^{2} - 5 x + 14$ as a set of factors.

$g (x) = (x + 2) (x^{2} - 6 x + 7)$

Write as a Set of Linear Factors g(x)=x^3-4x^2-5x+14

Related Questions

Support LCMGCF.com by disabling your adblocker.