Understanding Polynomial Factors

The video tutorial explains how to determine the value of c for which x-5 is a factor of a polynomial p(x). It begins by introducing the problem and encourages viewers to attempt solving it. The instructor then explains the concept of factorization and how to identify roots of a polynomial. By setting p(5) to zero, the instructor demonstrates the calculation process to solve for c, concluding that c equals -37. The tutorial provides a step-by-step approach to understanding polynomial factorization and solving related equations.

What is the main goal of the problem introduced in the video?

• To calculate the derivative of p(x)

• To find the maximum value of p(x)

• To determine the value of c for which x-5 is a factor of p(x)

• To find the value of x for which p(x) is zero

If x-5 is a factor of p(x), how can p(x) be expressed?

• As a quotient of x-5 and another polynomial

• As a sum of x-5 and another polynomial

• As a product of x-5 and another polynomial

• As a difference of x-5 and another polynomial

What must be true about p(5) if x-5 is a factor of p(x)?

• p(5) must be greater than zero

• p(5) must be equal to c

• p(5) must be less than zero

• p(5) must be equal to zero

What is the first step in solving for c after setting p(5) to zero?

• Differentiate p(x) with respect to x

• Calculate p(5) using the given polynomial

• Integrate p(x) with respect to x

• Find the inverse of p(x)

What is the value of c that makes x-5 a factor of the polynomial?

• 37

• -37

• 185

• -185