Answer: [tex](2a-5)(2a-1)[/tex]
Step-by-step explanation:
Given quadratic polynomial: [tex]4a^2-8a-5[/tex]
To factorize the given quadratic polynomial we use the "splitting of middle term" method that is the x term which is the sum of two factors and product equal to last term.
The product of first and last term =[tex]4a^2\times(-5)=-20a^2[/tex]
The middle term of the given polynomial can be written as
[tex]-10a+2a=-8a[/tex], where -10a and 2a are the factors of [tex]-20a^2[/tex].
Now, [tex]4a^2-8a-5\\=4a^2-10a+2a-5\\2a(2a-5)+1(2a-5)\\(2a-5)(2a-1)[/tex]
Hence, [tex]4a^2-8a-5=(2a-5)(2a-1)[/tex]
