Solve the following quadratic equation: x^2 + 3x + 2 = 0

Step 1: Find factors of the constant (The number with no x attached to it), In our case this is 2. The factors of 2 are: 1 & 2 and -1 & -2.

Step 2: The sum of the factors from step 1 must equal the number attached to the x term. In our case this is 3. Since -1 + (-2) = -3 these values cannot be correct. But, 1 + 2 = 3. So we know the factors must be 1 & 2.

(Trick to know which sign to use in the brackets: if the number on its own has a positive sign and the number attached to x had a positive sign then both brackets will have a positive sign. If the number on its own has a positive sign and the number attached to x had a negative sign then both brackets will have a negative sign. If the number on its own has a negative sign then one bracket will have a positive sign in it and the other a negative sign).

Step 3: We can now re write the equation inn afactorised form: This is (x+1)(x+2) = 0. To check if this is correct we can use the grid method to expand the brackets. This gives the original equation. (This would be shown on the whiteboard)

Step 4: For a final answer both of the brackets must be equal to zero. This gives: x+1 = 0 and x+2 = 0. We then re-arrange these to find x. The first expression gives x = -1 and the second gives x = -2. To check the answer we can substitute these x values into the starting equation.