Question

What is 5z²+19z-4 simplified?

Answer 1

Answer:

(5z-1)(z+4)

Explanation:

Given the expression:

$5z^2+19z-4$

Step 1: Multiply the first and last term

$5z^2\times-4=-20z^2$

Step 2: List out product pairs of -20z²

$\begin{gathered} -20z^2=-5z\times4z\colon-5+4=-1 \\ -20z^2=5z\times-4z\colon5-4=1 \\ -20z^2=-z\times20z\colon-1+20=19 \\ -20z^2=z\times-20z\colon1-20=-19 \end{gathered}$

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)