Find all the Zeros by Factoring a Polynomial to the 4th Power

The video tutorial discusses solving the equation X^4 - 625 by factoring. The instructor initially considers using the rational zero test and graphing but finds them cumbersome. Instead, the focus shifts to factoring, specifically using the difference of squares method. The equation is rewritten as a product of squares, and the zeros are found using the zero product property. The tutorial emphasizes the importance of recognizing factoring opportunities, especially with two or four terms, and concludes with a reminder to always consider factoring as a problem-solving strategy.

What is one method the speaker suggests to initially understand the zeros of the polynomial X^4 - 625?

• Using the rational zero test

• Graphing the polynomial

• Finding all factors of 625

• Using the quadratic formula

What is a key factorization technique mentioned for polynomials with two terms?

• Sum of cubes

• Difference of squares

• Sum of squares

• Difference of cubes

How can X^4 - 625 be rewritten using the difference of squares?

• (X^2 - 25)(X^2 + 25)

• (X^2 + 25)(X^2 + 25)

• (X^2 - 625)(X^2 + 625)

• (X^2 - 5)(X^2 + 5)

What is the zero product property used for in solving polynomial equations?

• To simplify the polynomial

• To find the degree of the polynomial

• To determine the leading coefficient

• To solve for the zeros of the polynomial

What are the zeros of the polynomial X^4 - 625 after factoring?

• ±25 and ±25i

• ±5 and ±5i

• ±10 and ±10i

• ±1 and ±1i