Find the Zeros of a Polynomial Then Write Out Using Linear Factorization

The video tutorial covers the process of finding rational zeros and factors of polynomials. It begins with an introduction to rational zeros and factors, followed by graphing techniques to identify zeros. The tutorial then explains the synthetic division process to find polynomial factors, including handling non-factorable problems. Finally, it discusses linear factorization and how to express polynomial factors in linear form.

What is the purpose of dividing the factors of the constant by the factors of the coefficient?

• To eliminate complex numbers

• To find the imaginary zeros

• To simplify the equation

• To determine the rational zeros

What is a common mistake students make during synthetic division?

• Ignoring the imaginary numbers

• Forgetting to multiply the coefficients

• Not maintaining place value

• Using the wrong divisor

How can you handle a polynomial that is non-factorable?

• Convert it to a quadratic equation

• Graph the polynomial

• Use synthetic division again

• Ignore the polynomial

What does linear factorization involve?

• Ignoring imaginary zeros

• Writing zeros as linear factors

• Expressing zeros as quadratic factors

• Combining all factors into a single term

What is the result of introducing a square root in an equation?

• It simplifies the equation

• It eliminates the imaginary part

• It introduces a plus or minus sign

• It becomes a complex number

Which of the following is a real zero found by graphing?

• X = 2

• X = 5

• X = -2

• X = ± I sqrt 2

What should you do if asked to write all zeros as linear factors?

• Ignore the imaginary zeros

• Express each zero as a linear factor

• Combine them into a single factor

• Use quadratic expressions