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

The video tutorial explains the process of finding zeros in polynomial functions, starting with the definition of zeros and moving through various factoring techniques. It covers factoring common terms, higher powers, and trinomials, and emphasizes the importance of verifying factored forms. The tutorial also discusses converting expressions to linear factors and understanding multiplicity, concluding with methods to identify zeros and their multiplicities.

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

• Set the function equal to zero

• Divide the function by x

• Rewrite the function in factored form

• Identify the highest power of x

How can you simplify the process of factoring expressions raised to the fourth power?

• By using the power rule

• By ignoring the exponents

• By considering them as quadratic problems

• By treating them as linear equations

What is a common mistake students make regarding multiplicity?

• Believing multiplicity is the power of the linear factor

• Thinking multiplicity is the power of the quadratic factor

• Confusing multiplicity with the degree of the polynomial

• Assuming multiplicity is always one

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

• Synthetic division

• Sum of cubes

• Difference of squares

• Quadratic formula

What are the zeros of the function after factoring X^2 - 1 and X^2 - 4?

• 0, ±1, ±2

• 0, 1, 2

• 1, 2, 3

• ±1, ±2, ±3

What is the multiplicity of the zeros after complete factorization?

• 2

• 1

• 3

• 4

What is the final step in writing the linear factorization of a function?

• Divide by the highest power of x

• Multiply all factors together

• Rewrite everything as linear factors

• Combine all terms into a single expression