Polynomial Evaluation and Factor Theorem

This video tutorial explains the factor theorem, which states that if a polynomial f(x) has a value of zero when a number p is substituted for x, then x minus p is a factor of the polynomial. The video provides several examples, including solving quadratic equations and demonstrating how to determine if expressions like x minus 2, x plus 3, two x minus one, and two x plus five are factors of given polynomials. The tutorial emphasizes the importance of substituting values into polynomials to verify factors and concludes with a summary of the factor theorem's application.

What is the Factor Theorem primarily used for?

• Solving linear equations

• Calculating derivatives

• Finding factors of polynomials

• Integrating functions

According to the Factor Theorem, if f(p) = 0, what can be concluded?

• p is a root of the polynomial

• x + p is a factor

• x - p is a factor

• p is a constant term

What does the Factor Theorem state about a polynomial f(x) if f(p) = 0?

• p is a coefficient

• x + p is a factor

• x - p is a factor

• p is a root

What does the Factor Theorem help determine about a polynomial?

• Its factors

• Its roots

• Its coefficients

• Its degree

What does the Factor Theorem help determine about a polynomial?

• Its degree

• Its factors

• Its roots

• Its coefficients

In the quadratic example, what are the factors of x^2 - 7x + 10?

• (x + 2)(x - 5)

• (x - 2)(x + 5)

• (x - 2)(x - 5)

• (x + 2)(x + 5)

What are the solutions for the equation x^2 - 7x + 10 = 0?

• x = 2 and x = -5

• x = 2 and x = 5

• x = -2 and x = 5

• x = -2 and x = -5

In the quadratic example, what operation is used to solve x^2 - 7x + 10 = 0?

• Integration

• Differentiation

• Factorization

• Simplification

In the quadratic example, what are the roots of x^2 - 7x + 10?

• x = 2 and x = 5

• x = -2 and x = 5

• x = 2 and x = -5

• x = -2 and x = -5

In the quadratic example, what are the roots of x^2 - 7x + 10?

• x = 2 and x = 5

• x = -2 and x = -5

• x = -2 and x = 5

• x = 2 and x = -5