Solving Polynomial Equations: Finding Solutions and Factoring

The video tutorial covers solving polynomial equations by finding solutions through factoring, substitution, and long division. It explains the remainder theorem and demonstrates how to find other solutions using these methods. The tutorial also explores advanced techniques for solving higher degree polynomials.

What are the factors of the polynomial X^2 + 7X + 12?

• X + 1 and X + 12

• X + 5 and X + 7

• X + 3 and X + 4

• X + 2 and X + 6

When evaluating F(x) = X^2 + 2X - 7 for X = 3 using substitution, what is the result?

• F(3) = 10

• F(3) = 8

• F(3) = 12

• F(3) = 5

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

• P(x)

• 0

• P(a)

• X - a

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

• X = 5 and X = -2

• X = 3 and X = -3

• X = 4 and X = -1

• X = 2 and X = -5

What is the other solution for the equation X^2 + 5X - 24 = 0 if one solution is X = 3?

• X = 5

• X = -3

• X = 8

• X = -8

What are the factors of the polynomial X^3 + 4X^2 - 15X - 18 if one solution is X = 3?

• 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 is the result of dividing X^3 + 4X^2 - 15X - 18 by X - 3?

• X^2 - 5X - 6

• X^2 + 7X + 6

• X^2 - 7X - 6

• X^2 + 5X + 6