How do you factor y=z^2 + 3z - 4 ?

1 Answer
Feb 22, 2016

Factors of z^2+3z−4 are $\left(z - 1\right) \left(z + 4\right)$

Explanation:

To find the factors of $a {z}^{2} + b z + c$, one should find factors of $a \cdot c$ whose sum is $b$.

As the function is z^2+3z−4, one should find factors of $1 \cdot \left(- 4\right)$ or $- 4$ whose sum is $3$.

These are $- 1$ and $4$. Hence splitting middle term this way.

z^2+3z−4 = z^2-1z+4z−4 or

$z \left(z - 1\right) + 4 \left(z - 1\right)$ or $\left(z - 1\right) \left(z + 4\right)$