Factor 30a^4+a^2-1

Math
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
Factor by grouping.
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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.
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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.
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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

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