# Expand the brackets. What are the missing coefficients?

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Expand the brackets. What are the missing coefficients?

Factorising Quadratics Know what does it mean to “factorise” quadratics. Understand how to factorise quadratics where there is a coefficient of x 2. Be able to Explain how the factorised form allows a quadratic equation to be solved.

Factorising Why? To find out which two algebraic linear expressions multiply to give you a quadratic. Linear expression: in the form of Quadratic: in the form of Polynomial of degree 2.

Factorising Expanding Opposite of Expanding / Multiplying

If you have x 2 – Easy Method If you have something like: (x 2 has a coefficient of 1) Rule 1 m and n have to multiple to give c Rule 2 Sum of m and n has to give b

Have a go Have a go at Q1 at the back, check your answers

You will be given quadratics to factorise that look like this: Algebraically, it’s factors look like this Factorising ax 2 + bx + c There’s just too much to deal with.

Factorising ax 2 + bx + c Clue 1 - ac is equal to jkmn Clue 2 - b is equal to (jn + km)

Factorising ax 2 + bx + c 1 – Find a common factor to take out (none in this case) 2 - (Using clues 1 & 2) Find two numbers that multiply to make ac, and add together to give b. Steps

Factorising ax 2 + bx + c 3 – write out your brackets with ax instead of x, along with your two numbers you found. Steps 4 – Simplify / take out any factors from brackets Took factor of 2 out Took factor of 3 out Factors are also factors of a

Factorising ax 2 + bx + c 1 – Find a common factor to take out (none in this case) 2 - Multiple c by a, then remove the a Steps 3 - Factorise this

Factorising ax 2 + bx + c 4 – divide each number in the brackets by a Steps 5 – Simplify these fractions to simplest form 6 – Multiple out the denominators

Factorising ax 2 + bx + c Steps 1 & 2 Steps 3 Steps 4 Steps 5 & 6

Factorising Circus 1) 2) 3) 4) 5) BONUS QUESTION

Factorising Circus 1) 2) 3) 4) 5) BONUS QUESTION

Quadratics = 0 When solving for quadratics equal to 0, one of the factors has to equal 0.

Quadratics = 0 When solving for quadratics equal to 0, one of the factors has to equal 0.

Have a go at Q3 Solve that quadratic!

Independent Study Exercise 4A p57-58 (solutions p418)