Finding All of the Zeros of a Polynomial Including Complex

The video tutorial covers the process of identifying factors of a polynomial, using the remainder and factor theorems to check for zeros, and exploring the factorization of cubic polynomials. It also discusses the quadratic formula for finding complex solutions and explains Descartes' rule of signs to determine the number of positive and negative real zeros in a polynomial.

What is the first step in testing potential factors of a polynomial without a calculator?

• Begin with positive 1 and then test negative 1

• Use the quadratic formula

• Start with the largest factor

• Check only the positive factors

Which theorem helps verify if a number is a factor of a polynomial?

• Pythagorean Theorem

• Binomial Theorem

• Factor Theorem

• Remainder Theorem

What is the result of synthetic division when testing if 1 is a factor?

• The remainder is 1

• The remainder is 0

• The remainder is 6

• The remainder is -1

What type of polynomial is being discussed in the factorization process?

• Quartic

• Cubic

• Linear

• Quadratic

What must be used when a polynomial is not factorable by simple methods?

• Graphical method

• Long division

• Quadratic formula

• Synthetic division

According to Descartes' Rule of Signs, what does one sign change indicate?

• One real positive zero

• Two real positive zeros

• No real zeros

• One complex zero

What does Descartes' Rule of Signs help determine?

• The sum of the coefficients

• The product of the roots

• The number of real zeros

• The degree of the polynomial