divided polynomials?

Question

what do you get when you divide 5a^2+6a-9 into 25a^4+19a^2-a-78

Answer 1

use long division
25a^4+19a^2-a-78 =
(5a^2+6a-9)(5a^2-6a +20) + (-175a+102)

5a^2+6a-9 )25a^4+19a^2-a-78 (5a^2-6a +20
less 25a^4+30a^3-45a^2
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-30a^3 +64a^2-a-78
less -30a^3-36a^2+54a
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100a^2 -55a-78
less 100a^2+120a-180
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-175a+102

so remainder is -175a+102

Answer 2

You get 5a^2 -6a - 20 with a remainder of 65a-258.
Just use long division or synthetic division.