Solving a Polynomial to Find all of the Zeros from the Factors

The video tutorial explains how to solve a polynomial equation by factoring. It begins with identifying the greatest common factor (GCF) and factoring the polynomial into binomials. The zero product property is then applied to find the zeros of the equation. The tutorial also covers solving for complex numbers and understanding the relationship between factors and zeros.

What is the first step in solving a polynomial equation by factoring?

• Set each factor to zero

• Factor out the greatest common factor

• Apply the zero product property

• Multiply all terms together

When factoring X^4 + 2X^2 + 1, what are the resulting binomials?

• (X + 1)(X + 1)

• (X^2 + 1)(X^2 + 1)

• (X^2 - 1)(X^2 - 1)

• (X + 2)(X + 2)

What is the purpose of the zero product property in solving polynomial equations?

• To find the zeros of the polynomial

• To simplify the polynomial

• To determine the degree of the polynomial

• To find the greatest common factor

What are the zeros of the polynomial X^5 + 2X^3 + X after factoring?

• 0, ±1

• 0, ±i

• ±1, ±i

• 0, ±2

How do factors relate to zeros in a polynomial equation?

• Zeros are added to find factors

• Factors are the same as zeros

• Zeros are found by setting factors to zero

• Factors are multiplied to find zeros