Quadratics - Null Factor Law

Quadratic

Expressions

Null Factor Law

Learning Goals

• Identify a quadratic equation

• Write a quadratic equation in standard form

• Apply the Null Factor Law to solve an equation in

factorised form

• A quadratic equation can be written

in the form

• This is called standard form, where

a , b and c are constants and a ≠ 0 .

Quadratic Equation

Examples

Multiple Choice

The standard form of a quadratic equation is

• y=x²

• y=ax²+bx+c

• y=mx+b

• y=x

Multiple Choice

Which of these quadratic expressions is in standard form?

• $$\left(x-3\right)^2-5=8$$

• $$3x^2+5x+2=0$$

• $$\left(x+7\right)\left(x-5\right)=0$$

• $$\left(3x+2\right)\left(x-9\right)=0$$

Multiple Choice

Factor x² + 12x + 20
WHAT TWO NUMBERS MULTIPLY TO 20
AND ADD UP TO 12? 

• (x + 2)(x + 10)
• (x + 7)(x + 5)
• (x + 6)(x + 6)

Multiple Choice

Which Quadratic equation is in Factored form?

• $$x^2+7x-18=0$$

• $$\left(x+7\right)\left(x-7\right)=0$$

• $$\left(x-8\right)^2+10=0$$

• $$15x^2+31x+2=0$$

Multiple Choice

The graph of a quadratic function is called

• a line
• a hyperbola
• a parabola
• a cubic

Null Factor Law

The Null Factor Law states that if the product of two
numbers is zero, then either or both of the two numbers is zero.

• If p × q = 0 then p = 0 or q = 0 .
• If (x + 1)(x − 3) = 0 then x + 1 = 0 (so x = −1 )

OR x − 3 = 0 (so x = 3 ).

Example

State the missing components to complete the following

working, which uses the Null Factor Law.

Multiple Choice

What is the correct solution/s for

$$\left(x+5\right)\left(x-7\right)=0$$  ?

• $$x=5,\ x=7$$  

• $$x=-5,\ x=-7$$  

• $$x=-5,\ x=7$$  

• $$x=5,\ x=-7$$  

• $$x=-35$$  

Multiple Choice

Solve for x using the Null Factor Law

$$x\left(x+15\right)=0$$  

• $$x=1,\ x=5$$  

• $$x=3,\ x=5$$  

• $$x=0,\ x=-15$$  

• $$x=0,\ x=15$$  

Multiple Choice

Solve for x using the Null Factor Law.

$$4x\left(x+10\right)=0$$  

• $$x=0,\ x=-10$$  

• $$x=0,\ x=10$$  

• $$x=10,\ x=4$$  

• $$x=0,\ x=-4$$  

Multiple Choice

Solve for x using the Null Factor Law.

$$\left(x+4\right)\left(3x-12\right)=0$$  

• $$x=-4,\ x=9$$  

• $$x=-4,\ x=4$$  

• $$x=3,\ x=-12$$  

• $$x=-4,\ x-3$$  

Multiple Select

Solve for x using the Null Factor Law.

$$\left(x+2\right)\left(x+2\right)=0$$  

• $$x=4$$  

• $$x=2$$  

• $$x=0$$  

• $$x=-2$$  

• $$x=-4$$  

Multiple Choice

Solve for x using the Null Factor Law.

$$\left(2x+4\right)\left(3x-9\right)=0$$  

• $$x=-4,\ x=0$$  

• $$x=-2,\ x=3$$  

• $$x=-4,\ x=3$$  

• $$x=9,\ x=-3$$  

Multiple Choice

Factorise, then solve:

$$x^2-5x=0$$

• $$x=-1,\ x=6$$

• $$x=2,\ x=3$$

• $$x=4,\ x=7$$

• $$x=0,\ x=5$$

Multiple Choice

Factorise then solve:

$$x^2-25=0$$

• x = 6 or x = -6
• x = 25 or x = -25
• x = 5 or x = -5
• x = 10 or x = -10

Your Turn!

Worksheet

OR

Q1, 2, 5, 6, 7, 8, 9 a), d) & g)

and Q11

Exercise

10A