Factorise x^2+6x-27
Label the three coefficients (each number, including an invisible 1 in from of the x2) as a, b and c.Think of it in two parts: a multiplied by c, which is just -27 in this example.The second part is just the 'b' term, which is 6.
So you need to think about and list the factors of -27 - what 2 numbers multiply to get -27.They are, -1 and 27, 1, and -27, 3 and -9, -3, and 9.What two of those numbers can add to make 6, or the 'b' term?-3 and 9. So they are your two numbers in the factorised term, so the answer is (x-3)(x+9)You should also check whether this is right by multiplying out again, using FOIL (first, outer, inner, last), to get our original answer, x2+6x-27.
BG
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