How to find the roots of a polynomials by factoring

The video tutorial covers factoring techniques for polynomials, starting with identifying the greatest common factor (GCF) and applying the zero product property. It then progresses to solving higher power polynomials by treating them as quadratic equations. The tutorial concludes with solving for the roots of the polynomial using square roots, emphasizing the importance of considering both positive and negative solutions.

What is the first step in simplifying the polynomial equation X^2 X^5 - 5X^3 + 4X = 0?

• Apply the zero product property

• Factor out the greatest common factor

• Solve for X directly

• Use the quadratic formula

After factoring out the GCF, what is the resulting equation?

• X^5 - 5X^3 + 4 = 0

• X^2 - 5X + 4 = 0

• X^3 - 5X + 4 = 0

• X^4 - 5X^2 + 4 = 0

How can you treat a higher power polynomial like X^4 - 5X^2 + 4 for easier factoring?

• As a linear equation

• As a constant

• As a quadratic equation

• As a cubic equation

What are the solutions to the equation X^2 - 4 = 0?

• X = ±2

• X = 4

• X = 0

• X = ±1

When solving X^2 = 1, why must both positive and negative roots be considered?

• To ensure all possible solutions are found

• Because the equation is linear

• To simplify the equation

• To apply the zero product property