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ULTIMATE MATHS

WHERE MATHS IS AT YOUR FINGERTIPS!

Example 1
We have solved the quadratic equation using factorisation. We
first factorised x and then checked which factors of 32 make 12
when added together (4&8). We have then put these factors into
the brackets before taking the values out of the brackets and
making them equal to 0. This allowed us to find the two possible
values of x.

Example 2
We have solved this quadratic equation by factorising it. We first
factorised 2x which is (2x+_)(x+_). Then we found the factors of 8.
Since we have 2x in the first bracket, we need to later on multiply
one of the factors by 2. This is why 4 and 2 work. If we put 4 into
the second pair of brackets, we will get 2 x 4 + 2 = 10. 10 is the
number we need to make 10x. Then we just finish solving the
equation as in the previous example just that we have to divide the
values that were in the first bracket by 2 since we want to find the
value of x and not 2x.

Example 1
In this first example, we are dealing with a simple quadratic
equation with only plus signs. We solved it by factorising x and
then finding the correct factors of 60 that give us 16x at the end.
Once we factorised the equation, we were able to solve it.

Example 2
This equation has a negative nx value but a positive number at the
end. As a result, bot brackets must contain a minus sign as we
need to multiply negative by negative to get a positive number.
After we found the correct factors of 16, we were able to solve the
equation.

Example 3
In example 3, we have a quadratic equation with a negative
number but a positive nx value. To solve it, we need to factorise
2x² and then find the correct factors of 12 before placing them in
the brackets considering the 2x² and the plus and minus signs.
The we can find the solution.

Example 4
In this last example, we have a quadratic in which both the nx
value and the number at the end is negative. To solve it, we must
find the correct pair of factors and place it in the brackets
considering the fact that we have a 2x² equation and the plus and
minus signs. Then we can deduct the solution.

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Chapter 17.1: Learning Outcomes
Students will learn how to solve simple quadratics (only positive) using
factorisation!
Students will learn how to solve complex quadratics (involving one or
more negatives) using factorisation!

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