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slega [8]
3 years ago
6

Factor the Higher degree polynomial 5y^4 + 11y^2 + 2

Mathematics
2 answers:
kotykmax [81]3 years ago
8 0

\bf 5y^4+11y^2+2\implies 5(y^2)^2+11y^2+2\implies (5y^2+1)(y^2+2)

RideAnS [48]3 years ago
5 0

For this case we must factor the following polynomial:

5y ^ 4 + 11y ^ 2 + 2

We rewrite y ^ 4as (y^ 2) ^ 2:

5 (y ^ 2) ^ 2 + 11y ^ 2 + 2

We make a change of variable:

u = y ^ 2

We replace:

5u ^ + 11u + 2

we rewrite the middle term as a sum of two terms whose product of 5 * 2 = 10 and the sum of 11.

So:

5u ^ 2 + (1 + 10) u + 2

We apply distributive property:

5u ^ 2 + u + 10u + 2

We factor the highest common denominator of each group.

(5u ^ 2 + u) + (10u + 2)\\u (5u + 1) +2 (5u + 1)

We factor again:

(u + 2) (5u + 1)

Returning the change:

(y ^ 2 + 2) (5y ^ 2 + 1)

ANswer:

(y ^ 2 + 2) (5y ^ 2 + 1)

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