The video tutorial explains the remainder theorem and its application in polynomial division. It introduces the factor theorem, highlighting its importance in determining polynomial factors. Through a practical example, the tutorial demonstrates how to factorize a polynomial and apply these concepts to graphing. The session concludes with a Q&A, addressing student queries and providing further insights into polynomial factorization.

What does the remainder theorem help you find when dividing a polynomial by a linear divisor?

• The leading coefficient

• The quotient

• The remainder

• The degree of the polynomial

According to the factor theorem, what does it mean if the remainder is zero when dividing a polynomial by x-a?

• The polynomial has no roots

• The polynomial is prime

• x-a is a factor of the polynomial

• x-a is not a factor of the polynomial

What is the first step in using the factor theorem to factorize a polynomial?

• Find the leading coefficient

• Graph the polynomial

• Test numbers to find a zero remainder

• Differentiate the polynomial

When using the factor theorem, why is it advised to start testing with smaller numbers?

• Smaller numbers are easier to calculate with

• Smaller numbers are always factors

• Smaller numbers always give a remainder of zero

• Larger numbers are not factors

What is the expected result when dividing a cubic polynomial by a linear factor?

• A quadratic polynomial with a remainder

• A cubic polynomial with no remainder

• A linear polynomial with a remainder

• A quadratic polynomial with no remainder

How does factorization help in graphing a polynomial?

• It identifies the leading coefficient

• It provides the y-intercept

• It gives the x-intercepts

• It determines the polynomial's degree

What does the leading coefficient of a polynomial indicate about its graph?

• The number of stationary points

• The y-intercept

• The direction of the graph

• The number of x-intercepts

Why might stationary points of a polynomial be difficult to find?

• They are always complex numbers

• They are not related to the polynomial's roots

• They require solving a quadratic equation

• They are always at the origin

What is a common characteristic of polynomials with integer roots?

• They have no x-intercepts

• Their stationary points are often non-integers

• They have no stationary points

• Their stationary points are also integers

If a polynomial has three factors, how many x-intercepts will it have?

• One

• Three

• Two

• Four