Question

Help with factorising quadratics

Answer 1

Well you did not say how you arrived at these wrong answers. You should be expanding your candidate answers to check them as well as checking for reasonableness, which these would fail. Twice you have swapped signs and once places.

Answer 2

1. I’m not sure how you’ve been taught to factorise quadratics, but I was taught to multiply a by c, in this case 3*10 which is 30. Then draw out (3a-15)(3a-2) for the  factors that add to get 17 and multiply to get 30. Then divide the one where both integers are divisible by 3. So it’ll turn out to be (3a-2)(a-5).

2. The same with 2, 11*-2 = -22, the factors that add to get -9 and multiply to get -22 are -11 and 2 (as -11+2=-9) so (11x-11)(11x+2) and then divide the divisible, so the answer’s (11x+2)(x-1)

3. the factors that add to get -2 and multiply to get -24 are -6 and 4, so (3y-6)(3y+4) then divide again (3y+4)(y-2)

You just have simple mistakes when it comes to mixing up signs, just write out your work carefully and you should be able to stop those mistakes. You can check your answers by solving for x, and then substituting it into your equation. if you get 0 you’re right

Answer 3

Always expand out your answers to check if you were correct. If you weren't maybe try swapping the numbers around to see if that works instead.

Answer 4

You can approach this multiple ways, rules or understanding. I prefer the latter.       
    
Take a simple example:    (x+1)(x+2) = x^2 + 3x + 2      
   
Lets look at it in steps:      
 
1. x^2 = x•x    

2. What positive numbers can you add to get 3, and multiply to get 2? That must be 1 and 2. Thus:  
  
3. x•1 + x•2 = x(1+2) = 3x     
    
4. 1•2 = 2     
    
Did this make sense to you? Break it down in steps and try to understand what it means.