I would like to begin this post by thanking my uncle Stephen 
You may be wondering... but how will this help? The answer to that is simple. School children will be able to use this tag to teach others about a certain topic/subject, find information that they require to complete a piece of homework that school has given them and could even act as a base for teachers to practise marking homework!
There are so many positives to draw from this new idea.
Objectives of this homework:
factorise - Putting an expression into brackets; the reverse process of expanding.
quadratic -contains a term that is squared. e.g 'x²'
bracket -Are used to make sure that operations are to be completed in an algebraic expression.
expression -phrase that contains numbers, operators and variables (e.g 4x-10)
solve -working out the answer
equation- The showing that two mathematical expressions are equal. (e.g 4x-1 = 2x+1)
1. x² + 5x + 6 = 0 The first thing you need to do when solving this quadratic equation is factorise.
the equation is factorised by following this method. In this instance, we need to find 2 numbers
that will add to get 5 but multiply to get 6. If it helps, you could list the factors down till you find a
matching pair. In this instance, these numbers will be 3 and 2. This is because 3+2=5 and 3 x 2=6
Always remember when solving a quadratic that you have two brackets with x in both of them.
(x+2) (x+3) =0 You'll be glad to know that you've done the hard bit! All you have to simply do now is to say how you
would make both the X's in the brackets equal to zero. Example, X+2=0. What would X have to be
inorder to make the equation equal to zero? The answer would be -2 because -2+2=0.
In conclusion the answer is : X= -2 X=-3
Let's try another example...
x² -14x +45 = 0 The method for factorising remains the same BUT this time we are dealing with a negative '-14x'.
This means that we are going to have to find 2 numbers that will add to make -14 but multiply to
make 45. Here are sum rules you need to be aware of when multiplying with numbers:
a minus number multiplied with another minus number = a positive number
a positive number multiplied with another positive number = a positive number
a minus number multiplied with a positive number = a negative number
a positive number multiplied with a negative number = a negative number
Therefore, knowing these rules, we can tell that both the numbers that are going to be in our
brackets are both negatives since 45 is a positive number.
(x-5) (x-9)=0 -9-5=14 and -9 x -5= 45
What numbers do the x's have to be to equal zero?
The answer is: X=5 x= 9
x² -3x - 36 = 4 Don't panic! It's easier than it looks.
1st step: take away four from one side of the equation to the other. This will make the equation on
one side of the equation equal to zero (the way we like it).
x²-3x-40 = 0 2nd step: now that the equation is equal to zero, we can factorise it. As the equation contains to
minus numbers, we will have to find a number that is negative and one number that is positive.
3rd step: find the factors that make add to make -3 and multiply to make -40.
(x+5) (x-8)=0 the numbers we need are are 5 and 8. This is because 5 +-8 = -3 and 5 x -8 = -40
4th step: What numbers do the x's have to be to equal zero?
The answer is X=-5 X= 8
Hope this was helpful.
Have a great weekend.
Jonathan :)
