Polynomial Equations and Their Solutions

This video tutorial covers solving polynomial equations, focusing on finding solutions through factoring, substitution, and long division. It explains the remainder theorem and its application in determining polynomial solutions. The tutorial also demonstrates solving quadratic and higher-degree polynomial equations, emphasizing the importance of understanding polynomial factors and zeros.

What is the first step in solving a polynomial equation like x^2 + 5x - 24 = 0?

• Finding the derivative

• Factoring the polynomial

• Using the quadratic formula

• Completing the square

Which pair of numbers are the factors of 12 that add up to 7 in the polynomial x^2 + 7x + 12?

• 5 and 2

• 3 and 4

• 2 and 6

• 1 and 12

What is the result of evaluating f(x) = x^2 + 2x - 7 for x = 3 using substitution?

• 10

• 12

• 8

• 5

According to the remainder theorem, what is the remainder when a polynomial p(x) is divided by x - a?

• x

• 0

• a

• p(a)

What are the zeros of the polynomial x^2 - 3x - 10?

• x = 5 and x = -2

• x = -5 and x = 2

• x = -5 and x = -2

• x = 5 and x = 2

What is the factorization of x^2 - 3x - 10?

• (x + 5)(x + 2)

• (x - 5)(x - 2)

• (x + 5)(x - 2)

• (x - 5)(x + 2)

When x^2 + 5x - 24 = 0 and one solution is x = 3, what is the other solution?

• x = 8

• x = -8

• x = -5

• x = 5

What is the first step in solving x^3 + 4x^2 - 15x - 18 = 0 when one solution is x = 3?

• Use synthetic division

• Perform long division by x - 3

• Use the quadratic formula

• Complete the square

What are the factors of the polynomial x^3 + 4x^2 - 15x - 18?

• (x - 3)(x + 6)(x + 1)

• (x + 3)(x - 6)(x - 1)

• (x - 3)(x - 6)(x - 1)

• (x + 3)(x + 6)(x + 1)

What are the zeros of the polynomial x^3 + 4x^2 - 15x - 18?

• x = -3, x = 6, x = 1

• x = 3, x = -6, x = -1

• x = -3, x = -6, x = 1

• x = 3, x = 6, x = 1