Question

Factor each polynomial by grouping. $$x y-3 y+x-3$$

   Factor each polynomial by grouping.
$$x y-3 y+x-3$$

Algebra for College Students

Algebra for College Students

Mark Dugopolski 5th Edition

Chapter 5, Problem 41

Instant Answer

Solved by Expert Amy Jiang

04/20/2020

Step 1

We can see that they have a common factor of $y$. So, we factor out $y$ from these two terms. $$y(x-3) + x - 3$$ Show more…

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Factor each polynomial by grouping. $$x y-3 y+x-3$$

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Key Concepts

Polynomial Factoring

This concept involves rewriting a polynomial as a product of simpler polynomials or factors. It is a fundamental process in algebra that simplifies expressions and solves equations, where the goal is to express the polynomial in a factored form, often making further analysis and problem-solving more manageable.

Factoring by Grouping

Factoring by grouping is a technique used to factor polynomials that have four or more terms. The method involves organizing terms into groups such that each group has a common factor, then factoring out those common factors to reveal a common binomial factor. This strategy applies the distributive property in reverse to simplify the expression.

Common Factor Extraction

This is the step of identifying and removing a common factor from two or more terms in an expression. In the context of factoring by grouping, extracting common factors from grouped terms is essential as it simplifies the expression and sets the stage for further factoring by revealing shared binomial factors.

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