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Learning objective overview
Master Teaching Guide coverage for this objective.
NA6-6
NZC26-P4-ALG-ER-P-Y10-01
Resources
- Dr Austin Maths - Factorising Revision Practice GridQuestions PDF · Answers
- CorbettMaths on factorising double brackets (when the leading coefficient is 1)Questions PDF · Answers
- Beta: Single brackets: Ex 9.04 to Ex 9.07, pgs 171 to 174
Terminology
- factorise
- double brackets
- constant
- adds to the middle, multiplies to the constant
- highest common factor (hcf)
- quadratic
- difference of two squares
- perfect square
- coefficient
- constant term
Task goals
- Factorise a quadratic $x^2+bx+c$ into two brackets when both numbers found are positive.
- Factorise a quadratic $x^2-bx+c$ into two brackets when both numbers found are negative.
- Fill in one or both missing numbers in a partially-given factorisation, such as $x^2+8x+15=(x+\square)(x+\square)$.
- Factorise a quadratic where the constant term is negative, so the two brackets have one positive and one negative number, such as $x^2+4x-12$ or $x^2-3x-10$.
- Decide whether a given factorisation is correct, or identify which of four expressions does not belong with the others.
- Explain why the two numbers used in the brackets must add to $b$ and multiply to $c$ in $x^2+bx+c$.
- Given the area of a rectangle as a quadratic expression and one side as a binomial factor, find the expression for the other side.
Where this fits
What leads into this objective, and where it goes next.
Before
Factorising single brackets
Expanding and Factorising Using the Distributive Law (Foundational)
Expanding and Factorising Algebraic Expressions
You are here
Factorising double brackets (with a leading coefficient of 1)
Simplifying and manipulating algebraic expressions involving sums, products, differences, and positive integer powers, by: collecting like terms; factorising using common factors; factorising quadratic expressions with a leading coefficient of 1; expanding products, including multiplying a single term by a bracketed term, and multiplying two expressions each of the form ax + b, where a and b are integers; factorising by grouping (i.e. using the distributive law) (e.g. x^2 + 2x − 8 = x^2 + 4x − 2x − 8 = x(x + 4) − 2(x + 4) = (x − 2)(x + 4))
Statement▸
Also under NA6-6:
For teachers
Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.