":"f782de55-c7a3-4a45-af34-440b9408a6c5","topicSlug":"factor-theorem","cards":[{"id":"069d473e-4023-495e-a034-aa40ba905775","cardType":"basic","front":"For $f(x)=2x^3-5x+4$, calculate $f(-2)$.","back":"$$f(-2)=\\strong{-2}$","points":1,"mcqOptions":null},{"id":"9c2d64f8-002f-4325-a0c9-4459a63cde4b","cardType":"basic","front":"Why should a substituted negative value be placed in brackets?","back":"Powers then apply to the whole negative value, e.g. $(-2)^2=4$.","points":2,"mcqOptions":null},{"id":"773c7a22-4cc2-46dd-b1ef-b8373c6f9cfc","cardType":"cloze","front":"When $f(x)$ is divided by $x-a$, the remainder is $\\text{[...]}$.","back":"When $f(x)$ is divided by $x-a$, the remainder is $\\boxed{f(a)}$.","points":null,"mcqOptions":null},{"id":"d8ccb5e8-5532-4751-94bb-71ff513243bc","cardType":"basic","front":"Find the remainder when $3x^3-2x^2+5$ is divided by $x-2$.","back":"$21$","points":1,"mcqOptions":null},{"id":"f7674a95-9b78-47f1-b289-e7eda5503e04","cardType":"cloze","front":"By the factor theorem, $x-a$ is a factor of $f(x)$ if and only if $\\text{[...]}$.","back":"By the factor theorem, $x-a$ is a factor of $f(x)$ if and only if $\\boxed{f(a)=0}$.","points":null,"mcqOptions":null},{"id":"ba58aa31-7fe5-498f-9087-658b25c01500","cardType":"basic","front":"What value should be substituted to test whether $x+5$ is a factor?","back":"Substitute $x=-5$.","points":1,"mcqOptions":null},{"id":"05f56352-b8ee-42ab-bdcf-86be9a47c025","cardType":"cloze","front":"To test whether $x+a$ is a factor, calculate $\\text{[...]}$.","back":"To test whether $x+a$ is a factor, calculate $\\boxed{f(-a)}$.","points":null,"mcqOptions":null},{"id":"e4c661b4-45de-4595-85e9-8edb0d771dac","cardType":"basic","front":"For $f(x)=x^3-3x^2-4x+12$, what proves that $x+2$ is a factor?","back":"$f(-2)=0$","points":1,"mcqOptions":null},{"id":"beb84271-71c3-4e01-b747-de0540c66b68","cardType":"basic","front":"If $f(4)=0$, which corresponding linear expression is a factor?","back":"$x-4$","points":1,"mcqOptions":null},{"id":"54d2273f-f804-4373-b475-dfb15631cb22","cardType":"basic","front":"If $x-3$ is a known factor of $f(x)$, what equation can determine an unknown coefficient?","back":"Use $f(3)=0$.","points":1,"mcqOptions":null},{"id":"9d89fbf0-b3f2-4ce9-b429-ba1c28a8f8ce","cardType":"cloze","front":"For a monic polynomial with integer coefficients, any integer zero must be a factor of the [ ].","back":"For a monic polynomial with integer coefficients, any integer zero must be a factor of the constant term.","points":null,"mcqOptions":null},{"id":"701420af-cb9c-4310-ad45-de8f3e166b0d","cardType":"basic","front":"Which integer values are candidates for zeros of a monic polynomial with constant term $6$?","back":"$\\pm1,\\ \\pm2,\\ \\pm3,\\ \\pm6$","points":1,"mcqOptions":null},{"id":"912a262c-1dcb-4cf4-9410-bf1b5ad72263","cardType":"basic","front":"Given $f(x)=x^3-2x^2-5x+6$ and $f(1)=0$, identify one factor.","back":"$x-1$","points":1,"mcqOptions":null},{"id":"37eba1af-48f1-4a9f-a9ab-888a9f934009","cardType":"basic","front":"Divide $x^3-2x^2-5x+6$ by $x-1$.","back":"The quotient is $x^2-x-6$.","points":2,"mcqOptions":null},{"id":"9c88239a-cfbf-4be7-b87a-a0973ad1135e","cardType":"basic","front":"Factorise $x^3-2x^2-5x+6$ fully.","back":"$(x-1)(x-3)(x+2)$","points":3,"mcqOptions":null},{"id":"dcc8eff4-63ed-473a-b7eb-2389181016f2","cardType":"basic","front":"Determine the zeros of $(x-1)(x-3)(x+2)$.","back":"$x=1,\\ 3,\\ -2$","points":1,"mcqOptions":null},{"id":"1062ed8b-5774-413b-9018-1d5e34864661","cardType":"cloze","front":"On $y=f(x)$, real zeros are the $x$-coordinates where the graph meets the

1.3.2 Factor theorem Flashcards

1.3.2 Factor theorem Flashcards