tiply to $\\boxed{ac}$ and add to $b$.","points":null},{"id":"36a71be6-171f-4bec-b194-ee6b3ce519b2","cardType":"cloze","front":"To factorise $ax^2+bx+c$, find two numbers that multiply to $ac$ and add to $\\text{[...]}$.","back":"To factorise $ax^2+bx+c$, find two numbers that multiply to $ac$ and add to $\\boxed{b}$.","points":null},{"id":"21c60a9c-117e-46b4-af8b-39fa6147c191","cardType":"basic","front":"If the constant term $c$ is positive and the $x$ coefficient $b$ is negative, what are the signs of the two numbers?","back":"Both are negative.","points":1},{"id":"24e0c065-4cd3-40c2-bafc-380459d8af77","cardType":"basic","front":"If the constant term $c$ is negative, what are the signs of the two numbers?","back":"One is positive and one is negative.","points":1},{"id":"8688ca13-fafd-42c1-9528-7e01f191cdb9","cardType":"basic","front":"What is the product target for splitting the middle term of $2x^2+x-15$?","back":"-30 ($2 \\times -15$)","points":1},{"id":"58b19766-58b8-4f69-b422-359165864a4d","cardType":"basic","front":"What is the sum target for splitting the middle term of $2x^2+x-15$?","back":"1","points":1},{"id":"324bc049-14e1-457a-b1a6-7c6390fe34dc","cardType":"basic","front":"Which two numbers multiply to $-30$ and add to $1$?","back":"6 and -5","points":2},{"id":"fc2dd0ab-947d-4440-afa7-7c5c596d667f","cardType":"cloze","front":"The expression $2x^2+x-15$ is split into $\\text{[...]}$ before grouping.","back":"The expression $2x^2+x-15$ is split into $\\boxed{2x^2+6x-5x-15}$ before grouping.","points":null},{"id":"f35fa4c0-7a70-4eb2-85af-ee6356d26dae","cardType":"basic","front":"When factorising by grouping, how do you check if your pair of numbers or signs are correct?","back":"Both parts of the expression must contain the same bracket.","points":1},{"id":"bf67db51-fb20-4ffd-ae6b-6a7fb948d24a","cardType":"cloze","front":"The zero product property states that if $AB=0$, then $\\text{[...]}$ or $B=0$.","back":"The zero product property states that if $AB=0$, then $\\boxed{A=0}$ or $B=0$.","points":null},{"id":"6ca1ca90-ee4e-4e45-a05d-df60e1cb0fdf","cardType":"cloze","front":"The zero product property states that if $AB=0$, then $A=0$ or $\\text{[...]}$.","back":"The zero product property states that if $AB=0$, then $A=0$ or $\\boxed{B=0}$.","points":null},{"id":"a91c93a3-59a3-4635-8bd0-3dd5de3ab613","cardType":"basic","front":"How do you find the roots of a quadratic equation once it is factorised into brackets?","back":"Set each bracket equal to zero and solve for $x$.","points":2},{"id":"63703ca2-c333-4c8d-bf98-d6e8e06e0796","cardType":"basic","front":"What are the solutions to $(2x-3)(2x+5)=0$?","back":"

$x=\\frac{3}{2}$
$x=-\\frac{5}{2}$

","points":2},{"id":"f702d6de-903c-41fe-b854-7b7d8119b7e3","cardType":"basic","front":"What two steps are required to factorise fully $6x^2-24$?","back":"

Take out the highest common factor 6
Use the difference of two squares on $(x^2-4)$

","points":2},{"id":"ca244182-2f78-4b9f-ba07-1187d0227da2","cardType":"cloze","front":"The difference of two squares formula is $a^2-b^2=$ $\\text{[...]}$.","back":"The difference of two squares formula is $a^2-b^2=$ $\\boxed{(a-b)(a+b)}$.","points":null},{"id":"6a0fdd90-a179-47b6-9382-2be83ee95fb6","cardType":"basic","front":"Factorise $x^2-4$.","back":"$$(x-2)(x+2)$","points":1},{"id":"1cf8e2d1-c80f-41bd-908f-e87bb8b084fb","cardType":"basic","front":"When factorising $2x^2+7xy+3y^2$, what variables must be present in the brackets?","back":"Both $x$ and $y$.","points":1},{"id":"6f66b311-b704-40c0-a3e0-06e371ea39a5","cardType":"basic","front":"Which numbers multiply to $12$ and add to $-13$ for the expression $3x^2-13xy+4y^2$?","back":"-12 and

Factorising Harder Quadratics Flashcards

Factorising Harder Quadratics Flashcards

Factorising Harder Quadratics Flashcards

Factorising Harder Quadratics Flashcards