Fractions involving Quadratic and Linear Terms: Non-Monic Expressions

Fractions involving Quadratic and Linear Terms Non-Monic Expressions


Now you can see that we can’t take 2 out because 2 is not a common factor for 5 and 3. So we’re just going to go straight to the cross method. But this time, it’s going to be x and 2x because x times 2x makes 2x squared, so it’s going to be a little bit different but again you should be very used to this. Now I’m going to start with 3, and you can see that if I cross it, I get 6x. So because I’ve used positive 3, the other one must be negative 1, isn’t it?

Because that’s a negative, so it’s going to be positive and negative. So x times negative 1 is negative x. Now you can see that 6x minus x is 5x and that’s what we want, so we’ve got the right factorization and I can factorize the numerator as x plus 3, 2x minus 1, okay? And you can see that we can cancel these out and we’ve just got 2x minus 1 left. Guys, I think it’s pretty repetitive now, see if you can try the next two on your own and just check your answer with me for those who can, okay?

What should we do guys? You can see that these numbers, 2 is a common factor, so first thing I would do is take the 2 out because that’s the common factor and now let’s factorize the inside part here. So we’ve got 12x squared, so what I’m going to do is use 3x and 4x. I could use 2x and 6x. But I’ll just try these first and if that doesn’t work I’ll use those that pair. So 6! We’ve got negative 6, so we’ll need a positive and a negative. So I’m going to start with positive 2 and see if we get it works out. 4x times 2 is 8x. So the other one must be negative 3, okay?

So that 3x times negative 3 is negative 9x and 8x minus 9x is negative x that is what we want which is right. Okay? So I’m going to put that inside the brackets, so it’s going to be 3x plus 2, 4x minus 3 there. And you can see the numerator 4x minus 3 denominators, same. So cross them out. So we’ve just got one there, make sure it’s not zero, it’s one some people tend to put zero for some reason. I cancelled that out. We have one left and then we’ve got 2 times 3x plus 2 left, okay?

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