Polynomials and rational expressions Flashcards","topicId":"62983eb8-2d6f-4be4-896a-2187ed73a10d","topicSlug":"polynomials-and-rational-expressions","cards":[{"id":"4429cba0-8a82-495a-a67e-9c4777d91b87","cardType":"cloze","front":"A polynomial term $ax^n$ requires [ ].","back":"A polynomial term $ax^n$ requires $n$ to be a non-negative integer.","points":null,"mcqOptions":null},{"id":"74e0faa2-1332-4dd1-94a6-aa88b7fcac49","cardType":"basic","front":"Why is $x^{-1}$ not a polynomial term?","back":"Its exponent is negative.","points":2,"mcqOptions":null},{"id":"43ac34f0-9e67-4741-945d-b18917a1ea1f","cardType":"basic","front":"What is the degree of $3x^4-2x^2+x-5$?","back":"4 - the highest power of $x$.","points":1,"mcqOptions":null},{"id":"633b527b-5e8f-44dd-a80d-f006f8bc7939","cardType":"cloze","front":"Terms can be collected only when they have [ ].","back":"Terms can be collected only when they have the same variable raised to the same power.","points":null,"mcqOptions":null},{"id":"4b20258e-8153-4a17-bb79-e88d9483f567","cardType":"basic","front":"Expand and simplify $(2x-3)(x^2+4x-5)$.","back":"$2x^3+5x^2-22x+15$","points":2,"mcqOptions":null},{"id":"5bf9d83f-5304-420a-aa3f-25e4f3b06eea","cardType":"basic","front":"What happens to the signs when a bracket is multiplied by a negative term?","back":"The sign of every term changes.","points":1,"mcqOptions":null},{"id":"fc9d4401-67b4-4e43-a0db-9d6aab9db0d7","cardType":"basic","front":"Factorise $6x^3-9x^2$ fully.","back":"$3x^2(2x-3)$","points":1,"mcqOptions":null},{"id":"cf1de94b-74b8-46bb-a626-42dddec5853b","cardType":"cloze","front":"The difference of two squares factorises as $\\text{[...]}$.","back":"The difference of two squares factorises as $\\boxed{a^2-b^2=(a-b)(a+b)}$.","points":null,"mcqOptions":null},{"id":"846ad71f-7d82-4f23-a374-13e1b438d6fb","cardType":"basic","front":"Factorise $6x^2+x-2$.","back":"$(2x-1)(3x+2)$","points":2,"mcqOptions":null},{"id":"95c40157-618a-4037-af8a-7ccf0c566672","cardType":"basic","front":"How can a polynomial factorisation be checked?","back":"Expand the factors to recover the original polynomial.","points":2,"mcqOptions":null},{"id":"93d0c5de-29da-44f4-b52c-20f957c74ea8","cardType":"cloze","front":"Polynomial division satisfies $\\text{[...]}$.","back":"Polynomial division satisfies $\\boxed{ext{dividend}=(\text{divisor})(\text{quotient})+\text{remainder}}$.","points":null,"mcqOptions":null},{"id":"da4202ea-fb61-49c8-a629-aeeea05bb525","cardType":"basic","front":"What type of remainder results from division by a linear expression?","back":"A constant remainder.","points":1,"mcqOptions":null},{"id":"d6fdd622-7f1b-4040-a4e0-98528fa473a6","cardType":"basic","front":"Divide $2x^3+3x^2-11x-6$ by $x+3$.","back":"$2x^2-3x-2$","points":2,"mcqOptions":null},{"id":"c20e6baf-7db2-4e83-9642-8aa1a42da723","cardType":"basic","front":"How should a missing power be handled during polynomial division?","back":"Insert a zero-coefficient term, such as $0x^2$.","points":2,"mcqOptions":null},{"id":"a6c51e77-e201-4384-90b3-7ee13a80debf","cardType":"cloze","front":"By the factor theorem, $x-a$ is a factor of $f(x)$ exactly when $\\text{[...]}$.","back":"By the factor theorem, $x-a$ is a factor of $f(x)$ exactly when $\\boxed{f(a)=0}$.","points":null,"mcqOptions":null},{"id":"a32f545a-0d59-44b8-ae5d-a6689af8e27d","cardType":"basic","front":"Which value should be substituted to test whether $x+2$ is a factor of $f(x)$?","back":"Substitute $x=-2$.","points":1,"mcqOptions":null},{"id":"ceb

1.5.6 Polynomials and rational expressions Flashcards

1.5.6 Polynomials and rational expressions Flashcards