Factorising Quadratic Trinomials using Common Factors and Rational Coefficients


Okay! I don’t like fractions guys. What do I do when I don’t like these fractions?

See guys if I want to rearrange this, well not rearranged. Kind of manipulate this, x squared over 12, it’s 1 over 12 x squared, isn’t it? If I just take if I just kind of separate with the x 12? x squared sorry. And this one the middle part here, 1 over 4 x and the last one I’ll just leave it as it is. So you can change it like this if you like So what’s the common factor guys? What’s the common factor is of 1 over 12, 1 over 4, and 1 over 3? I’m going to take out 1 over 12 out,
so this is just same as that, isn’t it?

I’m going to take 1 over 12 out so here I just have x squared so now it’s just monic and 1 over 4, I actually change it to 3 over 12, so I have the same denominator okay? If I keep it all in the same denominator with 12, see! 4 times 3 is 12, so I have to multiply the top by 3 as well. 3 times 4 is 12, so I have to multiply the top by 4 as well. See what I’m doing. So if I take out 1 over 12 out, here, I’ll just have 3 left, here, I’ll just have 4 left. So you can change it like this if you and it will help you a little bit more in factorizing fractions because fractions always confusing, don’t you? So that’s what I’ve done and then now let’s factorize the inside. There’s no more fractions which is excellent.

So I’ve got x and x, now 4, it’s going to be I’m going to use plus 1 and minus 4 because we need a negative and I know that 1 minus 4 is negative 3, so let’s just check that x, negative 4x, x minus negative 4x is negative 3x which is that. So keep the 1 over 12 out and we’ve got x plus 1 and x minus 4. That’s the answer, okay?

Question 28, we’ll also do it the same way but this time we have a bit of a decimal, don’t we? Now, in this section now main aim is to try to make it into a monic polynomial, isn’t it?
So what I’m going to do is factorize by 0.1. So take out the 0.1 and you just have x squared here. Now we know that 2 divided by 0.1. It’s 20, isn’t it? Basically, if you’re dividing by a decimal like this 0.1, you’re multiplying by 10. So this becomes 20 and this one becomes 91, okay? So now we’ll factorize that inside.

So we know that 13 and 7, I’m going to try and use 13 and 7 which is makes 91. If you didn’t really know that you might try to do a little bit of trial and error. So yeah spend some time finding the factors of 91 but I’m going to use 7 and 13 because I know that 7 plus 13 is 20. But my x’s on my left, I’m going to use negative 7 and negative 13 because we need negative 20 and this is positive.

So we’ll just check that becomes that and if negative 7 minus 13 is negative 20 which is this one here. So that’s pretty much it. x minus 7, x minus 13 with our 0.1 out the front, okay? So that was some non-monic quadratic polynomials sorry quadratic factorization, so basically trying to make it into a monic polynomial by taking out the common factor, okay? So that was pretty much it!


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