Solving quadratic equations by factorising | Maths | Quizalize & Oak National Academy

Starter quiz

Factorise the expression: $x^2 - 9x + 14$

'(x - 2)(x - 7)' ✓
Factorise the expression: $x^2 - 6x + 9$

$(x - 3)^2$ ✓

$(x + 3)^2$

$(x - 9)(x + 1)$
Factorise the expression: $16x^2 - 9$

'(4x - 3)(4x + 3)' ✓
Factorise the expression: $25y^2 - 64$

'(5y - 8)(5y + 8)' ✓
Factorise the expression: $4x^2 - 4x - 15$

'(2x - 5)(2x + 3)' ✓
Factorise the expression: $3x^2 + 12x + 12$

$3(x + 2)^2$ ✓

$3(x + 4)(x + 3)$

$(x + 4)^2$

Solve: $(x-4)(x+2)=0$

$x = 4, x = -2$ ✓

$x = 4, x = 2$

$x = -4, x = -2$
Solve: $x^2 - 5x + 6 = 0$

$x = 1, x = 6$

$x = 2, x = 3$ ✓

$x = 3, x = -2$
Solve: $2x^2 - 8x = 0$

$x = 0, x = 4$ ✓

$x = 0, x = -4$

$x = 4, x = -4$
Solve: $x^2 + x - 12 = 0$

$x = 2, x = 6$

$x = 3,x = -4$ ✓

$x = 4, x = -3$
Solve: $(2x-6)(x-9)=0$

$x = 3, x = -9$

$x = 3, x = 9$ ✓

$x =-3,x = 9$
Solve: $x^2 - 9x + 20 = 0$

$x = 3 , x = 7$

$x = 1, x = 20$

$x = 4, x = 5$ ✓

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The graph of a quadratic equation can show if there are solutions when the equation is equal to zero.
A quadratic might be the product of two binomial expressions.
If you find the two binomial expressions then you can find the values for x
The product is equal to zero, meaning that one of the two binomial expressions must equal zero.
You can set each expression to zero to find the value for x

That the solutions are just the constants in the binomials.

After factorising, pupils should be writing the one step equations, equal to zero, before writing the solutions.

Factorise - To factorise is to express a term as the product of its factors.
Solution (equality) - A solution to an equality with one variable is a value for the variable which, when substituted, maintains the equality between the expressions.
Parabola - A parabola is a curve where any point on the curve is an equal distance from: a fixed point (the focus ), and a fixed straight line (the directrix ).