Factoring Polynomials with the Factor Theorem

Mrs. A explains how to factor polynomial functions of degree higher than two, focusing on a degree 4 polynomial. The process begins with identifying common factors, followed by using the factor theorem to find polynomial factors. She demonstrates long division to verify factors and concludes with factoring a quadratic expression using decomposition. The video provides a step-by-step guide to simplifying and factoring complex polynomials.

What is the first step in factoring polynomials of degree higher than two?

• Apply the Factor Theorem

• Perform polynomial long division

• Extract common factors

• Use the quadratic formula

What is the common factor extracted from the polynomial in the tutorial?

• None of the above

• 3x

• 2x

• x

What does the Factor Theorem state about polynomial factors?

• None of the above

• If x - a is not a factor, then substituting a will zero the polynomial

• If x - a is a factor, then substituting a will zero the polynomial

• If x - a is a factor, then substituting a will not zero the polynomial

How do you verify if x - a is a factor of the polynomial?

• None of the above

• Multiply x - a by the polynomial and check for zero

• Divide the polynomial by x - a and check for a non-zero remainder

• Substitute a into the polynomial and check if the result is zero

What are the possible values of 'a' tested using the Factor Theorem in the tutorial?

• 1 and -1

• 1, -1, 2, -2

• 0, 1, -1

• 1, 2, 3, -3

What is the result of dividing a polynomial by one of its factors?

• Both B and C

• A quotient that is also a polynomial

• A remainder of 0

• A remainder of 1

What is the purpose of polynomial long division in the context of factoring?

• To find the derivative of the polynomial

• To confirm factors and find other factors

• To integrate the polynomial

• To simplify the polynomial

After factoring out the common factor and using the Factor Theorem, what is the next step?

• None of the above

• Factor by grouping

• Perform polynomial long division

• Apply the quadratic formula

What method is used to factor the quadratic part of the polynomial?

• Synthetic division

• Factor Theorem

• Common factor extraction

• Decomposition

What does decomposition involve in polynomial factoring?

• Breaking down a polynomial into irreducible factors

• Separating the polynomial into even and odd functions

• Finding two numbers whose product and sum fit the quadratic part

• Using synthetic division repeatedly