Factor each polynomial. See Examples 5 and 6. 9a2-16

Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

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Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 59

Chapter 1, Problem 59

Factor each polynomial. See Examples 5 and 6. 9a²-16

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Recognize that the polynomial \(9a^2 - 16\) is a difference of squares because it can be written as \((3a)^2 - 4^2\).

Recall the difference of squares factoring formula: \(x^2 - y^2 = (x - y)(x + y)\).

Identify \(x = 3a\) and \(y = 4\) in the expression \(9a^2 - 16\).

Apply the formula to factor the polynomial as \((3a - 4)(3a + 4)\).

Write the final factored form: \((3a - 4)(3a + 4)\).

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Key Concepts

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

Difference of Squares

The difference of squares is a special factoring pattern where an expression is written as a^2 - b^2. It factors into (a - b)(a + b). Recognizing this pattern helps simplify polynomials like 9a^2 - 16 by identifying perfect squares and applying the formula.

Perfect Squares

Perfect squares are numbers or expressions that are squares of integers or variables, such as 9a^2 (which is (3a)^2) and 16 (which is 4^2). Identifying perfect squares is essential to apply the difference of squares factoring method correctly.

Factoring Polynomials

Factoring polynomials involves rewriting a polynomial as a product of simpler polynomials. This process simplifies expressions and solves equations. Recognizing patterns like difference of squares is a key step in factoring efficiently.

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