Learn How to Solve a Polynomial Equation to a Higher Degree by Factoring

The video tutorial guides students through solving polynomial equations by setting them to zero, factoring, and finding zeros. It emphasizes the importance of factoring correctly and understanding the structure of polynomials, including identifying quadratic forms. The tutorial also addresses common student questions and provides step-by-step solutions to ensure comprehension.

What is the first step in solving a polynomial equation to find its zeros?

• Multiply all terms by two

• Divide all terms by the highest power

• Set the equation equal to one

• Set the equation equal to zero

When factoring a polynomial, why is it important to have the highest exponent term positive?

• It ensures the equation is quadratic

• It allows for easier addition of terms

• It simplifies the factoring process

• It makes the equation easier to read

What common factor is identified and factored out in the given polynomial?

• 12

• X

• X^3

• X^2

In the quadratic-like factoring process, what two numbers multiply to -12 and add to -1?

• 3 and -4

• -3 and 4

• 2 and -6

• -2 and 6

What is the next step after factoring the polynomial to find the zeros?

• Multiply the factors

• Add the factors together

• Set each factor equal to zero

• Divide the factors by the highest power

What are the zeros of the polynomial after solving the equation?

• 0, ±2, ±√4i

• 0, ±3, ±√2i

• 0, ±2, ±√3i

• 0, ±4, ±√3i

Why can't the square root of a negative number be taken in real numbers?

• It results in a positive number

• It results in an undefined value

• It results in a zero

• It results in a complex number