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Find the remainder when 8a^6+10a^4+2 is divided by a^2+3 by using remainder theorem

Find the remainder when 8a^6+10a^4+2 is divided by a^2+3 by using remainder theorem-example-1

1 Answer

5 votes
Replace
a^2=b. Then


8a^6+10a^4+2\equiv8b^3+10b^2+2

By the remainder theorem, the remainder upon dividing this polynomial by
a^2+3\equiv b+3 is given by the value of the polynomial where
b=-3. We have


8(-3)^3+10(-3)^2+2=8(-27)+10(9)+2=-124
User Georgy Buranov
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