How do you factorise a2-9a plus 18?

Answer 1

I'm assuming you meant a squared? (a^2)

If you did, then a^2-9a+18

For this, you need to know the FOIL rule (since a is squared).

(F=first O=outside I=inside L=last)

Start by drawing the brackets:

( ) ( )

You can also safely write a in the start in both brackets, because when you FOIL, you have to multiply the first numbers in the brackets first (F=first)

(a ) (a )

Now let's find the last numbers in the brackets! What two numbers, when multiplied, make 18?

18 x 1

9 x 2

6 x 3

Now, from these numbers, when either added or subtracted, which make 9 (the second number in your equation)? Obviously 6 and 3 (6+3=9)

So now, you can safely write the numbers into your brackets, the smallest number goes in the first bracket, the largest in the last.

(a 3) (a 6)

All you're missing is the signs! Now we use FOIL.

Multiply the first numbers: a x a = a^2

Multiply the outside numbers: a x 6 = 6a

Multiply the inside numbers: 3 x a = 3a

Multiply the last numbers: 3 x 6 = 18

Now you use your brain to see if 6a or 3a need to be positive or negative. To get -9a, you need to -6a -3a. So you're brackets would now look like this:

(a-3)(a-6) - And that's how you factorise!

You now also know that a = 3 or 6 (you have to invert the signs to get what a is equal to)