Name: Kaleena Who is asking: Other Level: Secondary Question: Factor this equation: 5x7-10x5+4x3-8x Hi Kaleena,The first feature I see in this expression is that every term has an x in it. That allows me to take out an x as a common factor. Hence 5x7 - 10x5 + 4x3 - 8x = x(5x6 - 10x4 + 4x2 - 8) What I see next is more subtile. I am going to group the terms because I see that 10 is twice 5 and 8 is twice 4. x(5x6 - 10x4 + 4x2 - 8) = x[(5x6 - 10x4) + (4x2 - 8)] In the first two terms inside the brackets take out a common factor of 5x4 and in the second two terms take out a common factor of 4. Thus x[(5x6 - 10x4) + (4x2 - 8)] = x[5x4(x2 - 2) + 4(x2 - 2)] Now the two terms inside the brackets have a common factor of x2 - 2. (This is the subtile observation I made when I observed that "10 is twice 5 and 8 is twice 4".) Thus x[5x4(x2 - 2) + 4(x2 - 2)] = x[(5x4 + 4)(x2 - 2)] A significant part of factoring is "pattern recognition". You need to be able to look at an expression and recognize something familiar. It's like hearing the first bar of a song and recognizing the group even if you haven't heard that exact song before. Harley Go to Math Central