Question

4n2 +5n-636=0
factorise this

Answer 1

Let .  is the coefficient of ,  is the coefficient of , and  is the constant. 

Find out two numbers that multiply to give  and add to give . 

Here,  and . 

So, in other words, we have to find two numbers that multiply to give -2544 and add to give 5 (or +5). 

Find out the factors of 2544. 

1 × 2544

2 × 1272

3 × 848

4 × 636

6 × 424

8 × 318

12 × 212

16 × 159

24 × 106

48 × 53

Now, check. It seems that if we add -48 and 53, we get five. 

(-48) × 53 = -2544 (= ac)

-48 + 53 = 5 (=b)

∴ The two numbers are -48 and 53. 

Now, in the given polynomial, suppose that 5n is the midde term. Break the middle term into two parts, such that their coefficients should be -48 and 53 and their variable should be the same, i.e., n.