k":"If $x=a$ is a root, then $(x-a)$ is a factor.","points":1},{"id":"2ef41b40-b351-4bbe-9d1d-06d537aa7d9e","cardType":"cloze","front":"If $x=-3$ is a root of a polynomial, the corresponding linear factor is $\\text{[...]}$.","back":"If $x=-3$ is a root of a polynomial, the corresponding linear factor is $\\boxed{x+3}$.","points":null},{"id":"20b1de7b-0707-490f-8b4f-69672e4c1916","cardType":"basic","front":"If $x = \\frac{1}{2}$ is a root of $f(x)$, what is the equivalent linear factor with integer coefficients?","back":"$$2x-1$","points":1},{"id":"b07bdfd9-abdd-4df3-8446-9f6f9566e094","cardType":"cloze","front":"The Factor Theorem states that the bracket $(x-a)$ is a factor of $f(x)$ if and only if $\\text{[...]}$.","back":"The Factor Theorem states that the bracket $(x-a)$ is a factor of $f(x)$ if and only if $\\boxed{f(a)=0}$.","points":null},{"id":"25cd0c79-bbc3-40b4-8376-d6eb7ee6a9c6","cardType":"basic","front":"To use the Factor Theorem to show $(x+2)$ is a factor of $f(x)$, what specific value must be substituted for $x$?","back":"$$-2$","points":1},{"id":"4df49057-435e-4d61-82ed-edddf6848507","cardType":"basic","front":"Where are the roots of a polynomial found on a graph of $y=f(x)$?","back":"The x-intercepts (where the curve crosses or touches the x-axis).","points":1},{"id":"4e8c6833-2543-4e34-9355-98f8e64bd69e","cardType":"basic","front":"In a cubic with integer coefficients, which term provides the candidate values for integer roots?","back":"The constant term (the number without an $x$).","points":1},{"id":"581f4083-7fa5-4080-9cd8-7be5a679549f","cardType":"cloze","front":"For the polynomial $f(x) = x^3 - 2x^2 + 5x + 6$, possible integer roots must be factors of [ ].","back":"For the polynomial $f(x) = x^3 - 2x^2 + 5x + 6$, possible integer roots must be factors of 6.","points":null},{"id":"5343ebb5-230a-4d12-a857-4cedbf999c0e","cardType":"basic","front":"According to exam technique, what two things must be shown to prove $(x-a)$ is a factor?","back":"

The substitution $f(a)$ calculated to equal 0
A conclusion stating that $(x-a)$ is a factor

","points":2},{"id":"ddfbfa07-e2d8-429b-8f88-1eb43f64e8dc","cardType":"basic","front":"What is the result of dividing a cubic polynomial by a linear factor?","back":"A quadratic expression.","points":1},{"id":"00e01d94-18bf-4447-b694-a306d853e879","cardType":"basic","front":"When factorising $f(x) = 2x^3 + ...$ into $(x-a)(Ax^2+Bx+C)$, how is the coefficient $A$ determined?","back":"By comparing the $x^3$ coefficients (in this case, $A=2$).","points":1},{"id":"896f839a-e30c-45b7-a8a4-c494df0d25c4","cardType":"cloze","front":"When substituting negative numbers into a polynomial, you should always use [ ] to avoid accuracy errors.","back":"When substituting negative numbers into a polynomial, you should always use brackets to avoid accuracy errors.","points":null},{"id":"a31d2dd0-ff9c-4372-ab15-ac232cd7b3d4","cardType":"basic","front":"If $f(x)$ contains two unknown constants $p$ and $q$, and you are given $f(1)=0$ and $f(2)=5$, what method is used to find $p$ and $q$?","back":"Simultaneous equations.","points":1},{"id":"6bb79346-1ab9-4066-932d-45ea5f1e03f0","cardType":"basic","front":"Outline the 3 standard steps to solve a cubic equation $f(x)=0$.","back":"

Find one root using the factor theorem
Divide by the matching linear factor to get a quadratic
Solve the quadratic (factorising or formula)

","points":3},{"id":"513ebce3-b40b-49b9-92e3-027ee8b65d2d","cardType":"cloze","front":"If a quadratic fact

7.3 The Factor Theorem Flashcards

7.3 The Factor Theorem Flashcards

7.3 The Factor Theorem Flashcards

7.3 The Factor Theorem Flashcards