교과서 질문
Factor each trinomial, if possible. See Examples 3 and 4. 36x3+18x2-4x
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0. Review of Algebra
Factoring Polynomials
1:17분문제 43
교과서 질문
In Exercises 1–68, factor completely, or state that the polynomial is prime. x² + 10x − y² + 25
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Identify the polynomial: \(x^2 + 10x - y^2 + 25\).
Rearrange the terms to group them: \((x^2 + 10x + 25) - y^2\).
Recognize that \(x^2 + 10x + 25\) is a perfect square trinomial, which can be factored as \((x + 5)^2\).
Rewrite the expression using the difference of squares formula: \((x + 5)^2 - y^2\).
Apply the difference of squares formula: \((a^2 - b^2) = (a - b)(a + b)\), where \(a = (x + 5)\) and \(b = y\), resulting in \((x + 5 - y)(x + 5 + y)\).
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1m주요 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 factoring out the greatest common factor, using special products like 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 presence of a difference of squares can simplify the factoring process, especially when combined with other terms.
추천 영상:
06:24Solving Quadratic Equations by Completing the Square
Completing the Square
Completing the square is a method used to transform a quadratic expression into a perfect square trinomial. This technique is useful for factoring and solving quadratic equations. In the context of the given polynomial, it can help identify the structure of the expression and facilitate the factoring process.
추천 영상:
06:24Solving Quadratic Equations by Completing the Square
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