Question

Factor using decomposition.4z^2 + 5z - 9

Answer 1

Given: A quadratic expression-

`4z^2+5z-9`

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-

`(1,36),(2,18),(3,12),(4,9),(6,6)`

Now we will take the pair (4,9) as

`\begin{gathered} 9-4=5 \\ 9*4=36 \end{gathered}`

Hence, rewriting the expression as-

`4z^2+9z-4z-9`

Taking the common term-

`z(4z+9)-1(4z+9)`

Hence the factorized expression is-

`(z-1)(4z+9)`

Final Answer: he

`(z-1)(4z+9)`