교과서 질문
Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. ƒ(x)=(x2-2x-3)/(2x2-x-10)
814
views
Ch. 3 - Polynomial and Rational Functions
Lial13th EditionCollege AlgebraISBN: 9780136881063
Not the one you use?Change textbookSelect a different textbook
Table of contents
4장, 문제 43
Solve each polynomial inequality. Give the solution set in interval notation. x4 + 2x3 + 36 < 11x2 + 12x
검증된 단계별 안내1
Rewrite the inequality by bringing all terms to one side to set the inequality to zero: \(x^{4} + 2x^{3} + 36 - 11x^{2} - 12x < 0\).
Combine like terms to simplify the expression: \(x^{4} + 2x^{3} - 11x^{2} - 12x + 36 < 0\).
Attempt to factor the polynomial \(x^{4} + 2x^{3} - 11x^{2} - 12x + 36\) by grouping or using substitution methods to find its roots.
Find the critical points by solving the equation \(x^{4} + 2x^{3} - 11x^{2} - 12x + 36 = 0\); these points divide the number line into intervals.
Test values from each interval in the original inequality to determine where the polynomial is less than zero, then express the solution set in interval notation.
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
8m도움이 되었나요?
주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Polynomial Inequalities
Polynomial inequalities involve expressions where a polynomial is compared to another value or polynomial using inequality signs (<, >, ≤, ≥). Solving them requires finding the values of the variable that make the inequality true, often by rewriting the inequality in standard form and analyzing the sign of the polynomial.
추천 영상:
06:07
Linear Inequalities
Factoring and Simplifying Polynomials
To solve polynomial inequalities, it is essential to rewrite the inequality so one side equals zero. This often involves moving all terms to one side and factoring the polynomial if possible. Factoring helps identify critical points where the polynomial changes sign, which are key to determining solution intervals.
추천 영상:
가이드 코스
07:30Introduction to Factoring Polynomials
Sign Analysis and Interval Notation
After finding critical points from the factored polynomial, sign analysis determines where the polynomial is positive or negative by testing values in each interval. The solution set is then expressed in interval notation, which concisely describes all values of the variable that satisfy the inequality.
추천 영상:
05:18Interval Notation
관련 실천
교과서 질문
Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=2x4+x3-6x2-7x-2
554
views
교과서 질문
Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. ƒ(x) = -3x2 + 18x + 1
803
views
교과서 질문
Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=2x3-5x2-x+6
995
views
교과서 질문
Solve each polynomial inequality. Give the solution set in interval notation. x5 + x2 + 2 ≥ x4 + x3 + 2x
489
views
교과서 질문
Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. ƒ(x) = -2x2 - 8x - 7
1625
views