How to factor a polynomial to the 5th power to find the zeros and multiplicity

The video tutorial explains how to find the zeros of a function and factor expressions, including those raised to higher powers. It emphasizes understanding the definition of zeros and the importance of rewriting expressions in factored form. The tutorial covers advanced factoring techniques, such as treating higher power expressions as quadratics, and clarifies common misconceptions about multiplicity and linear factorization. The instructor provides examples and encourages students to practice these techniques to improve their understanding.

What is the first step in finding the zeros of a polynomial function?

• Identify the degree of the polynomial

• Rewrite the function in factored form

• Find the derivative of the function

• Set the function equal to zero

When factoring a polynomial, what is the initial step to simplify the expression?

• Expand the polynomial

• Factor out common terms

• Use the quadratic formula

• Divide by the leading coefficient

How can a trinomial raised to the fourth power be approached for factoring?

• By applying the binomial theorem

• By using synthetic division

• By considering it as a quadratic

• By treating it as a linear equation

What is a common mistake students make regarding multiplicity of zeros?

• Not factoring completely

• Assuming multiplicity is always one

• Confusing power of terms with multiplicity

• Ignoring the degree of the polynomial

What is the correct multiplicity of zeros in a fully factored polynomial?

• The sum of all coefficients

• The number of terms in the polynomial

• The power of the linear factor

• The power of the polynomial

Which method can be used to factor expressions like X^2 - 1?

• Difference of two squares

• Completing the square

• Sum of cubes

• Quadratic formula

What are the zeros of the polynomial after complete linear factorization?

• 0, 1, 4

• 1, 2, 3

• 0, ±1, ±2

• ±1, ±4