How do you check a factorisation?

Expand the brackets and compare with the original.

To factorise x^2+bx+c, what do you look for?

Two numbers with product c and sum b.

Factorising expressionsIB MYP Maths Standard: Flashcards

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What does factorising mean?

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What does factorising mean?: Writing an expression as a product, the reverse of expanding.
Factorise fully $6x^2+9x$ .: $3x(2x+3)$
Factorise fully $8x^2-12x$ .: $4x(2x-3)$
How do you check a factorisation?: Expand the brackets and compare with the original.
Factorise $xy+3x+4y+12$ .: $(y+3)(x+4)$
State the difference of two squares.: $a^2-b^2=(a-b)(a+b)$
Factorise $x^2-49$ .: $(x-7)(x+7)$
Factorise $3x^2-75$ .: $3(x-5)(x+5)$
To factorise $x^2+bx+c$ , what do you look for?: Two numbers with product $c$ and sum $b$ .
Factorise $x^2+9x+20$ .: $(x+4)(x+5)$
Factorise $x^2+3x-10$ .: $(x+5)(x-2)$
Solve $(x-2)(x-3)=0$ .: $x=2$ or $x=3$
Simplify $\frac{x^2-9}{x+3}$ .: $x-3$

Exam questions on Factorising expressions

A rectangular banner has area $(x^2+9x+20)$ square centimetres. Its length and width are expressions in $x$ of the form $(x+p)$ and $(x+q)$ .
A second banner has area $(x^2+9x)$ cm $^2$ . Factorise this expression, and hence find the width of this banner when its length is $(x+9)$ cm.2 marks
A rectangular tile has area $(x^2-49)$ square centimetres.
Factorise fully $3x^2-75$ .2 marks
A rectangular vegetable bed has area $(x^2+3x-10)$ square metres and length $(x+5)$ metres, where $x>2$ .
Factorise $x^2+3x-10$ and hence write down an expression for the width of the bed.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).