Question

Facter each expression. $$3 z^{2}-15 t z+12 t^{2}$$

   Facter each expression.
$$3 z^{2}-15 t z+12 t^{2}$$

College Algebra

College Algebra

R. David Gustafson,… 11th Edition

Chapter 8, Problem 72

Instant Answer

Solved by Expert Amy Jiang

07/06/2020

Step 1

We can factor this out to simplify the expression: $$3 z^{2}-15 t z+12 t^{2} = 3(z^{2}-5tz+4t^{2})$$ Show more…

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Facter each expression. $$3 z^{2}-15 t z+12 t^{2}$$

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Key Concepts

Factoring Polynomials

Factoring polynomials involves rewriting an algebraic expression as a product of simpler polynomials. This is a key method used to simplify expressions, solve polynomial equations, and analyze the behavior of functions.

Greatest Common Factor (GCF)

Taking out the Greatest Common Factor is an essential step in polynomial factoring. It involves identifying and removing the largest factor common to each term, which simplifies the expression and makes the subsequent steps in the factoring process more straightforward.

Quadratic Factoring Techniques

Quadratic factoring techniques are used to factor quadratic expressions, typically of the form ax² + bx + c. Methods such as splitting the middle term or the AC method are employed to find two numbers that multiply to the product of the coefficient of the squared term and the constant term, and add to the coefficient of the linear term, facilitating the factoring of the quadratic expression into two binomials.

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