Given: A quadratic expression-
[tex]4z^2+5z-9[/tex]Required: To factorize using decomposition.
Explanation: To factorize using decomposition, we will look at the factor pairs of ac=36.
The factor pairs of 36 are-
[tex](1,36),(2,18),(3,12),(4,9),(6,6)[/tex]Now we will take the pair (4,9) as
[tex]\begin{gathered} 9-4=5 \\ 9\times4=36 \end{gathered}[/tex]Hence, rewriting the expression as-
[tex]4z^2+9z-4z-9[/tex]Taking the common term-
[tex]z(4z+9)-1(4z+9)[/tex]Hence the factorized expression is-
[tex](z-1)(4z+9)[/tex]Final Answer: he
[tex](z-1)(4z+9)[/tex]