Identify the Zeros and Their Multiplicities (x^3+2x^2-5x-6)/(x-2)

Math
To find the roots/zeros, set equal to and solve.
Find the LCD of the terms in the equation.
Tap for more steps…
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
The LCM is the smallest positive number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
The factor for is itself.
occurs time.
The LCM of is the result of multiplying all factors the greatest number of times they occur in either term.
Multiply each term by and simplify.
Tap for more steps…
Multiply each term in by in order to remove all the denominators from the equation.
Cancel the common factor of .
Tap for more steps…
Cancel the common factor.
Rewrite the expression.
Multiply by .
Solve the equation.
Tap for more steps…
Factor the left side of the equation.
Tap for more steps…
Factor using the rational roots test.
Tap for more steps…
If a polynomial function has integer coefficients, then every rational zero will have the form where is a factor of the constant and is a factor of the leading coefficient.
Find every combination of . These are the possible roots of the polynomial function.
Substitute and simplify the expression. In this case, the expression is equal to so is a root of the polynomial.
Tap for more steps…
Substitute into the polynomial.
Raise to the power of .
Raise to the power of .
Multiply by .
Add and .
Multiply by .
Add and .
Subtract from .
Since is a known root, divide the polynomial by to find the quotient polynomial. This polynomial can then be used to find the remaining roots.
Divide by .
Write as a set of factors.
Factor using the AC method.
Tap for more steps…
Factor using the AC method.
Tap for more steps…
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Remove unnecessary parentheses.
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Set the first factor equal to and solve.
Tap for more steps…
Set the first factor equal to .
Subtract from both sides of the equation.
Set the next factor equal to and solve.
Tap for more steps…
Set the next factor equal to .
Add to both sides of the equation.
Set the next factor equal to and solve.
Tap for more steps…
Set the next factor equal to .
Subtract from both sides of the equation.
The final solution is all the values that make true. The multiplicity of a root is the number of times the root appears.
(Multiplicity of )
(Multiplicity of )
(Multiplicity of )
(Multiplicity of )
(Multiplicity of )
(Multiplicity of )
Identify the Zeros and Their Multiplicities (x^3+2x^2-5x-6)/(x-2)

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Scroll to top