Answer: \((2a-5)(2a-1)\)
Step-by-step explanation:
Given quadratic polynomial: \(4a^2-8a-5\)
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 =\(4a^2\times(-5)=-20a^2\)
The middle term of the given polynomial can be written as
\(-10a+2a=-8a\), where -10a and 2a are the factors of \(-20a^2\).
Now, \(4a^2-8a-5\\=4a^2-10a+2a-5\\2a(2a-5)+1(2a-5)\\(2a-5)(2a-1)\)
Hence, \(4a^2-8a-5=(2a-5)(2a-1)\)
