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# AS maths c1 help watch

1. Hi guys, need help factorising this equation - also any tips on factorising equations that have a number in front of x^2 that would be very helpful and greatly appreciated! Thanks

4x^2-8x+3=0
2. Multiply the coefficient of x^2 term by get constant term. In other words multiply a by c to get ac. Then find 2 numbers that multiply to make ac but add to make b - the coefficient of the x term. Then split the x term into whatever these 2 numbers are. There should now be 4 terms in the expression. Now factorise the first 2 terms and then factorise the last 2 terms separately. You should find that there are 2 identical brackets. Then take out the expression in the brackets as a common factor and you should have factorised the quadratic into 2 linear factors.
I will give an example of this.
If we have 2x^2 + 9x + 10
We need to find 2 numbers that multiply to make 2*10 , 20 and add together to make 9 so we can see that the numbers 4 and 5 make this work.
Now we split the x term - 9x into the 2 numbers that we just found.
So 9x = 4x+5x
So the quadratic becomes
2x^2 + 4x+ 5x + 10
We factorise 2x^2 + 4x and 5x+10 separately
So we get 2x(x+2) +5(x+2)
So you see we have 2 identical brackets (x+2) common to both the 2x term and the constant term 5
Now if we take out (x+2) as a common factor we get (x+2)(2x+5)
So now we see that
2x^2 + 9x + 10 = (2x+5)(x+2)
3. (Original post by B_9710)
Multiply the coefficient of x^2 term by get constant term. In other words multiply a by c to get ac. Then find 2 numbers that multiply to make ac but add to make b - the coefficient of the x term. Then split the x term into whatever these 2 numbers are. There should now be 4 terms in the expression. Now factorise the first 2 terms and then factorise the last 2 terms separately. You should find that there are 2 identical brackets. Then take out the expression in the brackets as a common factor and you should have factorised the quadratic into 2 linear factors.
I will give an example of this.
If we have 2x^2 + 9x + 10
We need to find 2 numbers that multiply to make 2*10 , 20 and add together to make 9 so we can see that the numbers 4 and 5 make this work.
Now we split the x term 9x into the 2 numbers that we just found.
So 9x = 4x+5x
So the quadratic becomes
2x^2 + 4x+ 5x + 10
We factorise 2x^2 + 4x and 5x+10 separately
So we get 2x(x+2) +5(x+2)
So you see we have 2 identical brackets (x+2) common to both the 2x term and the constant term 5
Now if we take out (x+2) as a common factor we get (x+2)(2x+5)
So now we see that
2x^2 + 9x + 10 = (2x+5)(x+2)
typos
4. (Original post by YsfAli)
Hi guys, need help factorising this equation - also any tips on factorising equations that have a number in front of x^2 that would be very helpful and greatly appreciated! Thanks

4x^2-8x+3=0
The constant is prime so that makes it easier as we know the factors.
5. (Original post by )
typos
I was doing an example of a different quadratic so that I do not just give the answer as it is against forum rules.
6. (Original post by YsfAli)
Hi guys, need help factorising this equation - also any tips on factorising equations that have a number in front of x^2 that would be very helpful and greatly appreciated! Thanks

4x^2-8x+3=0
Hi,
I'll use a different example. 6x^2 - 7x - 3 = 0.

First of all, find two numbers that will multiply to give 3. The only possible combination is 3 and 1. These go here:
( 3)( 1)= 0

Next find two numbers that multiply to give 6. There are two possible combinations: 3 and 2 OR 6 and 1.

Also, because the 3 has a minus in front of it, one of the brackets needs to have a plus and the other a minus, so that when you expand the brackets, you get the -3 term.
You now try out the possible combinations until it works.

The answer comes out to be (3x -1)(2x + 3)=0

Note that sometimes you cannot factorise using this method and you need to use the quadratic formula or completing the square method instead.

Your equation will work using the method I showed above.
Hope this helps!
7. (Original post by B_9710)
I was doing an example of a different quadratic so that I do not just give the answer as it is against forum rules.
You said 4 and 5 multiply to give 20 and add to give 7, that's wrong; it's not a different quadratic its simply wrong.
8. (Original post by )
You said 4 and 5 multiply to give 20 and add to give 7, that's wrong; it's not a different quadratic its simply wrong.
Oh yeah. It's because I started off doing a different example but changed halfway through and forgot about the 7
9. (Original post by Angel28)
Hi,
I'll use a different example. 6x^2 - 7x - 3 = 0.

First of all, find two numbers that will multiply to give 3. The only possible combination is 3 and 1. These go here:
( 3)( 1)= 0

Next find two numbers that multiply to give 6. There are two possible combinations: 3 and 2 OR 6 and 1.

Also, because the 3 has a minus in front of it, one of the brackets needs to have a plus and the other a minus, so that when you expand the brackets, you get the -3 term.
You now try out the possible combinations until it works.

The answer comes out to be (3x -1)(2x + 3)=0

Note that sometimes you cannot factorise using this method and you need to use the quadratic formula or completing the square method instead.

Your equation will work using the method I showed above.
Hope this helps!
That actually makes more sense to me as my teacher doesn't really bother explaining little things in detail. Thanks a lot really do appreciate it!
10. (Original post by B_9710)
Multiply the coefficient of x^2 term by get constant term. In other words multiply a by c to get ac. Then find 2 numbers that multiply to make ac but add to make b - the coefficient of the x term. Then split the x term into whatever these 2 numbers are. There should now be 4 terms in the expression. Now factorise the first 2 terms and then factorise the last 2 terms separately. You should find that there are 2 identical brackets. Then take out the expression in the brackets as a common factor and you should have factorised the quadratic into 2 linear factors.
I will give an example of this.
If we have 2x^2 + 9x + 10
We need to find 2 numbers that multiply to make 2*10 , 20 and add together to make 9 so we can see that the numbers 4 and 5 make this work.
Now we split the x term - 9x into the 2 numbers that we just found.
So 9x = 4x+5x
So the quadratic becomes
2x^2 + 4x+ 5x + 10
We factorise 2x^2 + 4x and 5x+10 separately
So we get 2x(x+2) +5(x+2)
So you see we have 2 identical brackets (x+2) common to both the 2x term and the constant term 5
Now if we take out (x+2) as a common factor we get (x+2)(2x+5)
So now we see that
2x^2 + 9x + 10 = (2x+5)(x+2)
Totally get it now. Thanks so much!!
11. (Original post by YsfAli)
That actually makes more sense to me as my teacher doesn't really bother explaining little things in detail. Thanks a lot really do appreciate it!
No problem!

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