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

Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 59

1장, 문제 59

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

검증된 단계별 안내

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: \((3a - 4)(3a + 4)\).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.