교과서 질문
In Exercises 1–68, factor completely, or state that the polynomial is prime.
x² − 12x + 36 − 49y²
1002
views
0. Review of Algebra
Factoring Polynomials
1:37분문제 27
교과서 질문
In Exercises 1–30, factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. x² + xy + y²
검증된 단계별 안내1
Identify the trinomial: \(x^2 + xy + y^2\).
Check if the trinomial can be factored by looking for two binomials \((ax + by)(cx + dy)\) that multiply to give the original trinomial.
Consider the structure of the trinomial: it resembles a perfect square trinomial, which is typically of the form \((x + y)^2 = x^2 + 2xy + y^2\).
Notice that the middle term \(xy\) is not twice the product of \(x\) and \(y\), which suggests that this trinomial might not be a perfect square.
Conclude that \(x^2 + xy + y^2\) is a prime trinomial because it cannot be factored into simpler polynomials with integer coefficients.
비슷한 문제에 대한 검증된 영상 답변:이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
1m주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Factoring Trinomials
Factoring trinomials involves rewriting a quadratic expression in the form ax² + bx + c as a product of two binomials. This process requires identifying two numbers that multiply to ac (the product of a and c) and add to b. Understanding this concept is crucial for simplifying expressions and solving equations.
추천 영상:
6:29
Factor Using Special Product Formulas
Prime Trinomials
A prime trinomial is a quadratic expression that cannot be factored into the product of two binomials with rational coefficients. Recognizing when a trinomial is prime is essential, as it indicates that the expression cannot be simplified further. This concept helps in determining the nature of the roots of the quadratic equation.
추천 영상:
05:20Expanding Radicals
FOIL Method
The FOIL method is a technique used to multiply two binomials, standing for First, Outside, Inside, Last, which refers to the order in which the terms are multiplied. This method is also useful for checking the accuracy of a factorization by ensuring that the product of the binomials returns to the original trinomial. Mastery of FOIL is important for verifying solutions in algebra.
추천 영상:
03:07FOIL
관련 영상
관련 실천