Question

Factor completely. $$6 z^{2}+42 z+72$$

   Factor completely.
$$6 z^{2}+42 z+72$$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Sherri Messersmith 2nd Edition

Chapter 7, Problem 64

Instant Answer

Solved by Expert Julie Silva

06/29/2020

Step 1

The GCF of $6z^{2}$, $42z$, and $72$ is $6$. So, we factor out $6$ from the expression. $$6z^{2}+42z+72 = 6(z^{2}+7z+12)$$ Show more…

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Factor completely. $$6 z^{2}+42 z+72$$

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Key Concepts

Factoring Quadratic Expressions

This concept revolves around rewriting a quadratic expression as a product of two binomials. It leverages techniques such as finding two numbers that multiply to the constant term and add up to the coefficient of the linear term, thereby breaking down the quadratic into manageable factors.

Common Factor Extraction

This concept involves identifying and removing any common factors shared by all terms in an expression. It simplifies the process of factoring by reducing the coefficients and making the resulting quadratic or polynomial easier to work with.

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