 Quandaries and Queries Who is asking: Student Level: Secondary Question: I'm in FST and I am so confused and we have a test coming up soon. I have these practice problems that I don't know what to do, and I was hoping someone could help me out. I put what I think it should be next to it, so you mabye can tell me whats wrong, if anything. Here they are: Factor these: x3+125 -----> (x+5)3 8x3-27 -----> (?) x2+36 -----> (x+6)2 x4-5x2+4 --> (?) Any shortcuts are appreciated. I'm usually pretty good in math, but I just can't grasp this, I just don't get it. Thanks! KJ Hi KJ, There are some patterns that you need to recognize to in order to factor. Three if these patterns are: the difference of squares a2 - b2 = (a - b)(a + b) the difference of cubes a3 - b3 = (a - b)(a2 + ab + b2) and the sum of cubes a3 + b3 = (a + b)(a2 - ab + b2). For example, in your first problem, 125 = 53 and thus this is a sum of cubes x3+125 = x3 + 53 = (x + 5)( x2 - 5x + 25) In a similar way your second problem is a difference of cubes. Problem 3 doesn't match any of the three paterns above, in fact the exprerssion in problem 3 can't be factored. Problem 4 is again recognizing a pattern. When I look at problem 4 I see (quantity 1) - 5 (quantity 2) + 4 where (quantity 1) is the square of (quantity 2) To be more formal. Let y = x2 then x4-5x2+4 = y2 -5y + 4 Factor this expression then replace y by x2 and see if the resulting expression can be further factored. Penny Go to Math Central