1.5 Factorisation  (Page 2/2)

There are some tips that you can keep in mind:

• If $c$ is positive, then the factors of $c$ must be either both positive or both negative. The factors are both negative if $b$ is negative, and are both positive if $b$ is positive. If $c$ is negative, it means only one of the factors of $c$ is negative, the other one being positive.
• Once you get an answer, multiply out your brackets again just to make sure it really works.

Factorising a trinomial

1. Factorise the following:

   (a) $x^2+8x+15$	(b) $x^2+10x+24$	(c) $x^2+9x+8$
   (d) $x^2+9x+14$	(e) $x^2+15x+36$	(f) $x^2+12x+36$

2. Factorise the following:
   1. $x^2-2x-15$
   2. $x^2+2x-3$
   3. $x^2+2x-8$
   4. $x^2+x-20$
   5. $x^2-x-20$
      
      
3. Find the factors for the following trinomial expressions:
   1. $2x^2+11x+5$
   2. $3x^2+19x+6$
   3. $6x^2+7x+2$
   4. $12x^2+8x+1$
   5. $8x^2+6x+1$
      
      
4. Find the factors for the following trinomials:
   1. $3x^2+17x-6$
   2. $7x^2-6x-1$
   3. $8x^2-6x+1$
   4. $2x^2-5x-3$
      
      

Factorisation by grouping

One other method of factorisation involves the use of common factors. We know that the factors of $3x+3$ are 3 and $(x+1)$ . Similarly, the factors of $2x^2+2x$ are $2x$ and $(x+1)$ . Therefore, if we have an expression:

then we can factorise as:

You can see that there is another common factor: $x+1$ . Therefore, we can now write:

We get this by taking out the $x+1$ and seeing what is left over. We have a $+2x$ from the first term and a $+3$ from the second term. This is called factorisation by grouping .

Factorisation by grouping

1. Factorise by grouping: $6x+\mathrm{a}+2ax+3$
   
2. Factorise by grouping: $x^2-6x+5x-30$
   
3. Factorise by grouping: $5x+10y-ax-2ay$
   
4. Factorise by grouping: $a^2-2a-ax+2x$
   
5. Factorise by grouping: $5xy-3y+10x-6$