0
x2 -7x +6=0 can be factorised by looking at the 7 and the 6 and looking for two numbers that can both add to give -7 and can multiply to give +6.
Possible factors for (numbers that will multiply to give) 6 are:
2 & 3
1 & 6
Now look at the possible sums from these possible factors:
2+3=5 not 7, and making one or more of these negative still won't result in a sum of 7 so we can rule those out.
1+6=7 Good so far! Now look at the sign. We need a negative 7. If both the 1 and the 6 are negative, it will give -7, which is what we are looking for.
-1 x -6 =6 because the two negatives cancel out, which is what we need, so the quadratic can be factorised as:
(x-1)(x-6)=0
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