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ULTIMATE MATHS

WHERE MATHS IS AT YOUR FINGERTIPS!

Example 1
To factorise this linear equation, we found the lowest
common factor which is 5 and put it outside the brackets.
Then we have divided 10x and 25 by 5 and used the
solutions as the values inside the brackets.

Example 2
To factorise this linear equation, we have found the lowest
common factor which is 7 and placed it outside the
brackets. We have then divided 14x and -28 by 7 which gave
us the values inside the brackets. In this problem, we have a
minus sign inside the bracket.

Example 1
To factorise this quadratic equation, we
had to make the 2x² by putting 2x into a
bracket and x in the other. We identified
that to get a negative x value and a
positive number we must have two
negative factors. We tried all factors and
ended up with -5 and -3. This works as
-5 x -3 = 15 and -5x - 6x = -11x. We get -6
because we have to multiply -3 by 2x and
not just by x. The equation is now
factorised.

Example 2
Factorising this quadratic equation is a lot
easier as we only have x² and a negative
square number. We start of by butting x in
both brackets again. Then we we just
have to put the square root of 9 (3)
negative in one bracket and positive in
the other. Like this we end up with
-3 x +3 = -9 and -3x + 3x = 0x. This is
called the “difference of two squares”.
Factorising these types of equations is
very easy.

Example 3
To factorise this quadratic equation, we
again started of by making x² by putting x
in each pair of brackets. Due to the fact
that the number (20) is negative, we have
to have one positive and one negative
factor. We ´discovered that 4 and -5 works
as 4 x -5 = -20 and 4x - 5x = -x. The
equation is now factorised.

It is very important that you always remember to make sure that you have the right numbers negative and positive. Also ensure that you always consider
the number in front of the x² in certain equations where there is one.

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Chapter 15.0: Learning Outcomes
Students will be introduced to the concept of factorisation!
Students will learn how to factorise linear equations
Students will learn how to factorise quadratic equations!

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