3z2+4z+1

Factor 4 out of 4z.

3z2+4(z)+1

Rewrite 4 as 1 plus 3

3z2+(1+3)z+1

Apply the distributive property.

3z2+1z+3z+1

Multiply z by 1.

3z2+z+3z+1

3z2+z+3z+1

Group the first two terms and the last two terms.

(3z2+z)+3z+1

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

z(3z+1)+1(3z+1)

z(3z+1)+1(3z+1)

Factor the polynomial by factoring out the greatest common factor, 3z+1.

(3z+1)(z+1)

Factor 3z^2+4z+1