5v2+4v-1

Factor 4 out of 4v.

5v2+4(v)-1

Rewrite 4 as -1 plus 5

5v2+(-1+5)v-1

Apply the distributive property.

5v2-1v+5v-1

5v2-1v+5v-1

Group the first two terms and the last two terms.

(5v2-1v)+5v-1

Factor out the greatest common factor (GCF) from each group.

v(5v-1)+1(5v-1)

v(5v-1)+1(5v-1)

Factor the polynomial by factoring out the greatest common factor, 5v-1.

(5v-1)(v+1)

Factor 5v^2+4v-1