A short recorded GCSE maths lesson (YouTube transcript) by Paul from Third Space Learning on factorising quadratics when a=1. The video explains the core method: find two numbers that multiply to the constant term C and add to the linear coefficient B, illustrates with worked examples (x^2+8x+15 → (x+3)(x+5); x^2-6x+8 → (x-2)(x-4); x^2+3x-18 → (x-3)(x+6)), and gives marking guidance for typical 2-mark exam questions. The video closes by pointing viewers to more resources and one-to-one tuition.
Questions this video answers
Paul from Third Space Learning.
(x + 3)(x + 5).
(x - 2)(x - 4).
(x - 3)(x + 6).
Chapters
Hi, this is Paul from Third Space Learning. And today we're going to look at factorizing quadratics into two brackets. Now a quadratic is just an algebraic expression in the form AX squared plus BX plus C. The highest power there is 2, and we're going to factorize them when A is 1. Now, factorizing just means to put into brackets, which is the opposite of of expanding brackets. As usual, I'll use our online classroom to go to the topic and look at some questions. Check out the links at the end of the video for access to tons of free resources, practice questions and information on our one to one personalised tuition. Okay, let's have a look at factorizing quadratics. When A is one, grab a pen and let's dive in. Let's start by factorizing the quadratic in the form ax squared plus bx cubed when a is 1. So all we have to do here is find two numbers that multiply to give the end number C and add to give the middle number B. So for example, if we had x squared plus 8 x 15, we need two numbers that multiply together to give 15 and the same two have to add to give 8. Well, 3 times 5 is 15, 3 add 5 is 8. So we have our numbers. All we do now is open up a pair of double brackets and put an X at the start of one and at the start of the other one because X is the variable, the letter. And then put the plus three and the plus five in the brackets. And that's it, all done, fully factorized. So let's have a look at a few questions together to see how this works in practice. Factorise X squared. Take away 6x plus 8. Now a, here is one. Remember, a is the coefficient of the x squared. It's the number in front of it and it's actually just a one. So we need two numbers that will multiply to give positive eight and add to give negative six. So let's start then by writing out the factors of eight. Well, that's 1 and 8 and 2 and 4. So I need a pair of those, either 1 and 8 or 2 and 4 that will multiply to give a positive answer. Well, I know that if a positive multiplied by a positive gives me a positive and a negative multiplied by a negative gives me a positive, that means that the signs must be the same if I want to multiply and get a positive answer. So they'll both be negative or both be positive. But these numbers also need to together to give this negative six so that tells me the numbers are probably going to be both negative. So let's choose our pair. Let's go over this 1, 2 and 4 and we've got a negative 2 and a negative 4. And let's see if that works. Well, if I add Those together, negative 2 add negative 4 is the same as negative 2, subtract 4, which is negative 6. So that works. And let's see if minus 2 and negative 4 work when we multiply. Well, minus 2 multiplied by negative 4 is positive 8, which is exactly what I want. So that works brilliantly. So that means our numbers are negative 2 and negative 4. All we have to do then is open up a pair of brackets, pop in the X because the variable is X, the letter used here is X, and then use our numbers. So negative two and negative four. And there we go, fully factorized. Now we could write them in the other other way around if we wanted to. X take away 4, x take away 2, that's the same thing. But that is a perfect answer. So let's see where the marks come from. Well, we're going to get one mark for writing down x and a 2 with some sort of sign and x and a 4 with some sort of sign. So even if you get the signs in the brackets wrong, you can still pick up a mark. But we want full marks. So the second mark comes from getting both negatives correct. And that is a two mark question. Okay, let's have a go at this question. Pause the video and have a go. Best of luck. Okay, let's go through it. So it says factorize x squared plus 3x take away 18. And we can see that this is a quadratic one where a is 1. So the coefficient of x squared, the number in front of it is 1. So all we have to do is find two numbers that multiply to give negative 18 and the same two numbers that have to add to give 3. So let's start by writing out the factors of 18. So we got 1 and 18, 2 and 9 and 3 and 6. Now we need a pair of these that will multiply to give a negative answer, right? Well, we know that positive times a negative will give me a negative answer and also a negative times a positive will give me a negative answer. So that tells me the signs must be different. So let's choose our factor pair. Well, because we want them to add to give that positive three. This three and six look quite good. The only question is where do the signs go? So is it negative three and positive six or Positive three and negative six. Well, if we have negative three and positive six and we add those together, thinking of the number line, we jump to the right and we get a positive three. So that works. Let's make sure that when we multiply them, we get the answer we need. Negative 18. Well, three multiplied by six is 18 and a negative multiplied by a positive is a negative. So that works as well. So we have our numbers. They are negative 3 and positive 6. Great. So all we have to do now is open up a pair of brackets and we put an X at the start of them both because X is a variable here, the letter and then we put the numbers in. So minus three in one and positive six in the other one. Take great care to make sure that we get the signs the right way around. And there we go. Full marks, fully factorized. But let's see where the marks come from. So there's one mark here. If you put an X and a 3 with some sort of sign in one bracket and an X and a 6 with some sort of sign in the other bracket. So even if you mess up the signs, you might get one mark. So that's good news. But we're out of full marks. So the second mark is for getting the answer fully correct. X subtract three in one bracket and x plus six in the other bracket. Two marks. Thanks so much for watching the video. Check out the description below for loads more information on this topic and for access to our library of free online resources and loads of information on our one to one tuition. Don't forget to like and subscribe to stay up to date with all the latest third space learning videos.
