Question

What is 5z²+19z-4 simplified?

Answer 1

(5z-1)(z+4)

Step-by-step explanation:

Given the expression:

`5z^2+19z-4`

Step 1: Multiply the first and last term

`5z^2*-4=-20z^2`

Step 2: List out product pairs of -20z²

`\begin{gathered} -20z^2=-5z*4z\colon-5+4=-1 \\ -20z^2=5z*-4z\colon5-4=1 \\ -20z^2=-z*20z\colon-1+20=19 \\ -20z^2=z*-20z\colon1-20=-19 \end{gathered}`

Step 3: Pick the pair that sums up to the middle term (-z and 20z) and use it to replace the middle term.

`5z^2+19z-4=5z^2+20z-z-4`

Step 4: Factorize

`\begin{gathered} =5z\mleft(z+4\mright)-1\mleft(z+4\mright) \\ =\mleft(5z-1\mright)\mleft(z+4\mright) \end{gathered}`

The simplified form is: (5z-1)(z+4)