Factor by any method. See Examples 1–7. 4z^4-7z^2-15

Key Concepts

Factoring Polynomials

Factoring polynomials involves rewriting a polynomial expression as a product of simpler polynomials. This process is essential for simplifying expressions and solving equations. Common methods include factoring out the greatest common factor, using the difference of squares, and applying the quadratic formula for quadratic expressions.

Quadratic Form

The expression 4z^4 - 7z^2 - 15 can be viewed as a quadratic in terms of z^2. By substituting u = z^2, the polynomial transforms into 4u^2 - 7u - 15, which can be factored using techniques for quadratic equations. Recognizing this form is crucial for applying appropriate factoring methods.

Zero Product Property

The Zero Product Property states that if the product of two factors equals zero, at least one of the factors must be zero. This principle is vital when solving polynomial equations after factoring, as it allows us to set each factor equal to zero to find the solutions for the variable.