Factorise x^3+3x^2-x-3
Test factors of -3 to find a root for the equation. For example, try 1, 1^3+3*1^2-1-3=0, so 1 is a root, and (x-1) is a factor. Now it's known that: (ax^2+bx+c)(x-1)=x^3+3x^2-x-3. By comparing coefficients for x^3 term, a=1, and for x^0 term, c=3. Then for the x term, c-b=-1, so b=4. Therefore the original equation equals (x^2+4x+3)(x-1). Now factorise the quadratic to give (x+3)(x+1)(x-1). Expanding the bracket again can be used to check your answer.
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