Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Factoring Polynomials

College Algebra

0. Review of Algebra

Factoring Polynomials

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2:22 minutes

Problem 7

Textbook Question

In Exercises 1–68, factor completely, or state that the polynomial is prime. x²y − 16y + 32 − 2x²

Verified step by step guidance

Combine like terms: x^2y and -2x^2 to get (x^2y - 2x^2) and -16y + 32.

Factor out the greatest common factor from each group: x^2(y - 2) and -16(y - 2).

Notice that (y - 2) is a common factor in both terms.

Factor out the common factor (y - 2) from the expression: (y - 2)(x^2 - 16).

Recognize that x^2 - 16 is a difference of squares and can be factored further as (x - 4)(x + 4).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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 techniques include factoring out the greatest common factor, using special products like the difference of squares, and applying the quadratic formula when necessary.

Identifying Prime Polynomials

A polynomial is considered prime if it cannot be factored into the product of two non-constant polynomials with real coefficients. Recognizing prime polynomials is crucial in algebra, as it helps determine the limits of simplification and the methods needed for solving polynomial equations.

Combining Like Terms

Combining like terms is the process of simplifying an expression by adding or subtracting terms that have the same variable raised to the same power. This step is often necessary before factoring, as it helps to organize the polynomial into a standard form, making it easier to identify potential factors.