30a4+a2-1

Rewrite a4 as (a2)2.

30(a2)2+a2-1

Let u=a2. Substitute u for all occurrences of a2.

30u2+u-1

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=30⋅-1=-30 and whose sum is b=1.

Multiply by 1.

30u2+1u-1

Rewrite 1 as -5 plus 6

30u2+(-5+6)u-1

Apply the distributive property.

30u2-5u+6u-1

30u2-5u+6u-1

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(30u2-5u)+6u-1

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

5u(6u-1)+1(6u-1)

5u(6u-1)+1(6u-1)

Factor the polynomial by factoring out the greatest common factor, 6u-1.

(6u-1)(5u+1)

(6u-1)(5u+1)

Replace all occurrences of u with a2.

(6a2-1)(5a2+1)

Factor 30a^4+a^2-1