To factorise is to express a term as the product of its factors.

A solution to an equality with one variable is a value for the variable which, when substituted, maintains the equality between the expressions.

Solving quadratic equations by factorising where rearrangement is required

Maths

In this unit, pupils learnt to solve quadratic equations by factorising and this skill will be required in the future unit through manipulating two simultaneous equations to find the solutions. For pupils studying the higher content, solving quadratic equations is required if one of the simultaneous equations is a quadratic.

In the prior unit, pupils used the distributive law to find the product of two binomials. In algebraic manipulation, pupils use apply this knowledge in order to factorise quadratics.

Algebraic manipulation

Find the value of $$x$$ where: $$x^2 = 6x - 9$$

Find the value of $$x$$ where: $$x^2 = 4x - 4$$

Find the values of $$x$$ where: $$5x = x^2 - 6$$

Factorise the expression $$x^2 + 2x - 15$$

Which of these is a solution for: $$(x - 4)(x + 2) = 0$$

Which of these is a solution for: $$(x + 2)(x - 5) = 0$$

Which of these is a solution for: $$(x + 9)(x + 3) = 0$$

Which of these is a solution for: $$(x - 6)^2 = 0$$

Factorise the expression $$7x^2 + 42x - 49$$

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