13. factor completely: $2x^{2}+3x - 2$ 14. factor completely: $5x^{2}-36x + 7$

Explanation:

Step1: Factor $2x^{2}+3x - 2$

For a quadratic $ax^{2}+bx + c$ (here $a = 2$, $b=3$, $c=-2$), we need to find two numbers that multiply to $ac=-4$ and add up to $b = 3$. The numbers are 4 and - 1. Rewrite the middle - term: $2x^{2}+4x - x - 2$. Group the terms: $(2x^{2}+4x)-(x + 2)$. Factor out the common factors from each group: $2x(x + 2)-(x + 2)$. Factor out $(x + 2)$: $(2x-1)(x + 2)$.

Step2: Factor $5x^{2}-36x + 7$

For the quadratic $ax^{2}+bx + c$ (here $a = 5$, $b=-36$, $c = 7$), we need to find two numbers that multiply to $ac = 35$ and add up to $b=-36$. The numbers are -35 and -1. Rewrite the middle - term: $5x^{2}-35x-x + 7$. Group the terms: $(5x^{2}-35x)-(x - 7)$. Factor out the common factors from each group: $5x(x - 7)-(x - 7)$. Factor out $(x - 7)$: $(5x - 1)(x - 7)$.

Answer:

13. $(2x - 1)(x + 2)$
14. $(5x - 1)(x - 7)$