5x^2-7x-6 please help me to solve the question
Answers
5x² - 7x - 6
By middle term splitting,
5x² - 10x + 3x - 6
= 5x(x-2)+3(x-2)
= (x-2)(5x+3)
This is your required answer.
More about middle term splitting:-
Middle term splitting is the process in which the middle Term is splitted in to two factors in such a way that their product is equal to the product of 1st term and last term.
E.g.-----> If we take the equation provided by you
5x² - 7x - 6
In this equation 7x is the middle term which need to be splitted into two factors in such a way that the product of the two factors is equal to the product of 1st term (i.e. 5) and last term (i.e. 6).
So in order to do so we will first multiply the 1st term and the last term. Then factorise it and find that factors which when added will give the middle term.
In this case,
We will multiply the first term and the second term.
1st term = 5
2nd term = -6
Therefore, 5×-6 = -30
All possible factors of 30 = 1,2,3,5,6,10,15,30.
So If we take 10 and 3
We have to add it in such a way that the result will be -7
So we will take it as -10 and +3
Now see we on multiplying these two numbers will get -30 as product.
Now we have splitted the middle term.
so the equation now becomes:-
5x² - 10x + 3x -6
Now taking terms in common
From 5x² and 10x we can take 5x as common and from 3x - 6 we can take 3 as common.
So,
5x(x-2)+3(x-2)
Now we can see we got two same terms i.e x-2
So taking x-2 in common again.
(x-2)(5x+3) Becomes our answer.
Hope this helps you.....