This is in the form Ax^2+Bx +C where A=1 B=2 and C=-3 We need to find two numbers (let's call them p and q) which multiply to equal C and add to equal B. Since C is negative we need a positive number and a negative number. In this case we can say p=-1 and q=3 since -1*3=-3=C and -1+3=2=B Now we split B into p and q in the original formula so it becomes x^2-x+3x-3 We can then factorise it in two parts

x^2-x: divide each part by x to get x(x-1) -3x-3: divide each part by 3 to get 3(x-1) We can then add these two parts together x(x-1)+3(x-1). The bit in brackets (x-1) forms one factor and the bit outside (x+3) forms another. The final factorisation is (x-1)(x+3). We can check this is correct by expanding the brackets again.

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