to make $\\text{[...]}$ and add to make $b$.","back":"When factorising $x^2 + bx + c$ (where $a=1$), find two numbers that multiply to make $\\boxed{c}$ and add to make $b$.","points":null},{"id":"a0b6de37-6e24-4b14-b414-ee9200012d8e","cardType":"cloze","front":"When factorising $x^2 + bx + c$ (where $a=1$), find two numbers that multiply to make $c$ and add to make $\\text{[...]}$.","back":"When factorising $x^2 + bx + c$ (where $a=1$), find two numbers that multiply to make $c$ and add to make $\\boxed{b}$.","points":null},{"id":"815b6b80-7bb6-4cc7-928c-2a9c94f049e8","cardType":"basic","front":"What is the first step in the split the middle term method for $ax^2 + bx + c$?","back":"Multiply the coefficient $a$ by the constant $c$.","points":1},{"id":"4f99b2d8-400a-4016-8f76-9915859a3a0f","cardType":"cloze","front":"In the expression $ax^2 + bx + c$, the numbers used to split the middle term must multiply to $\\text{[...]}$ and add to $b$.","back":"In the expression $ax^2 + bx + c$, the numbers used to split the middle term must multiply to $\\boxed{ac}$ and add to $b$.","points":null},{"id":"db6ea213-10a5-42a3-977e-f73d3902a23f","cardType":"cloze","front":"In the expression $ax^2 + bx + c$, the numbers used to split the middle term must multiply to $ac$ and add to $\\text{[...]}$.","back":"In the expression $ax^2 + bx + c$, the numbers used to split the middle term must multiply to $ac$ and add to $\\boxed{b}$.","points":null},{"id":"dd692529-1cfb-4732-87e8-69539fd66dc2","cardType":"basic","front":"In $ax^2 + bx + c$, what signs must the split numbers have if $c$ is negative?","back":"One positive and one negative.","points":1},{"id":"f3bb5f0b-4f19-4d0b-8fbd-ccc0a210f980","cardType":"basic","front":"In $ax^2 + bx + c$, what signs must the split numbers have if $c$ is positive but $b$ is negative?","back":"Both numbers must be negative.","points":1},{"id":"7345f649-9b63-4651-b092-246d7149132e","cardType":"basic","front":"List the steps to factorise $ax^2 + bx + c$ by grouping after splitting the middle term.","back":"

Factorise the first two terms
Factorise the last two terms
Take out the common bracket

","points":3},{"id":"b39e89f2-d636-4681-b1a8-71f288cccbb6","cardType":"basic","front":"How can you mentally check if your factorisation is correct?","back":"Expand the brackets; the result should match the original expression.","points":1},{"id":"816f1e62-9dd2-4424-8d80-5effc07b204a","cardType":"basic","front":"What is the Zero Product Property?","back":"If $AB = 0$, then $A = 0$ or $B = 0$.","points":1},{"id":"68fdff61-0daf-4c8f-90bd-7ef34641206c","cardType":"basic","front":"What is the next step to solve $(3x - 2)(x + 4) = 0$ after factorising?","back":"Set each bracket to zero: $3x - 2 = 0$ and $x + 4 = 0$.","points":1},{"id":"693cbf02-e923-4741-ab0c-8ec4f2445560","cardType":"cloze","front":"If an exam question asks you to factorise fully, the first thing you should check for is a [ ].","back":"If an exam question asks you to factorise fully, the first thing you should check for is a common factor.","points":null},{"id":"46ba863f-c445-4250-8b73-b8814d9477f0","cardType":"basic","front":"State the identity for the difference of two squares.","back":"$$A^2 - B^2 = (A - B)(A + B)$","points":1},{"id":"78067a96-65ca-496b-8de6-1a26c6790d4e","cardType":"basic","front":"Factorise $3x^2 - 75$ fully.","back":"$$3(x - 5)(x + 5)$","points":2},{"id":"ea6c6759-4670-42ab-b8e2-3d814c810688","cardType":"cloze","front":"To factorise $2x^2 + 11xy + 5y^2$, find two numbers that multiply to [ ] and add to 11.","back":"To factorise $2x^2 + 11xy + 5y^2$, find

Factorising Harder Quadratics Flashcards

Factorising Harder Quadratics Flashcards

Factorising Harder Quadratics Flashcards

Factorising Harder Quadratics Flashcards