factorise

Question

7x^2 - 19x + 10

13x - 20 - 2x^2

28n - 10 + 6n^2

please can you show me the method

thanks

Answer 1

for the first one, you first find the factors of 7 ...the only possibility is (7)*(1)=7 so you have

(7x +/- ?)(x +/- ?)

next you would consider the factors of ten
(1)(10)=10
(2)(5)=10
note that you also must consider negatives here! so -1,-10,-2,&-5 are also possibilities!

now, look at the factors of 10 and determine what will give you -19 ... so basically, (7x)*(?)+(x)*(?)=-19
after trial and error you will be able to see that the correct answer is as follows

(7x-5)(x-2)

check you answer by expanding

(7x)(x) +(7x)(-2) + (-5)(x) + (-5)(-2)
=7x^2 -14x-5x +10
=7x^2 -19x +10