교과서 질문
Factor out the greatest common factor from each polynomial. See Example 1. 2(m-1)-3(m-1)2+2(m-1)3
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0. Review of Algebra
Factoring Polynomials
3:44분문제 25
교과서 질문
In Exercises 1–68, factor completely, or state that the polynomial is prime. x² − 12x + 36 − 49y²
검증된 단계별 안내1
Identify the polynomial: \(x^2 - 12x + 36 - 49y^2\).
Recognize that the expression can be rearranged as \((x^2 - 12x + 36) - 49y^2\).
Notice that \(x^2 - 12x + 36\) is a perfect square trinomial, which can be factored as \((x - 6)^2\).
Rewrite the expression as \((x - 6)^2 - (7y)^2\).
Apply the difference of squares formula: \(a^2 - b^2 = (a - b)(a + b)\), where \(a = x - 6\) and \(b = 7y\), to factor the expression as \((x - 6 - 7y)(x - 6 + 7y)\).
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3m주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
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 identifying common factors, using the difference of squares, and applying the quadratic formula when necessary.
추천 영상:
07:30
Introduction to Factoring Polynomials
Difference of Squares
The difference of squares is a specific factoring pattern that applies to expressions of the form a² - b², which can be factored into (a + b)(a - b). In the given polynomial, recognizing the structure of a difference of squares is crucial for simplifying the expression effectively.
추천 영상:
06:24Solving Quadratic Equations by Completing the Square
Quadratic Expressions
A quadratic expression is a polynomial of degree two, typically written in the form ax² + bx + c. Understanding the properties of quadratic expressions, including their graphs and roots, is vital for factoring them. In this case, recognizing that the expression can be rearranged into a quadratic form aids in the factoring process.
추천 영상:
06:36Solving Quadratic Equations Using The Quadratic Formula