Mathematics: Find the remainder of (h^4+h^2-2)/(h+3)

Find the remainder of (h^4+h^2-2)/(h+3) - id4223163006, adamskhan990

Ответ:

jjel18

10.03.2022

Mathematics

(-3)^4+(-3)^2-2=88 , so by the polynomial remainder theorem, the remainder is 88.

To verify this, we can compute the quotient remainder:

$h^4=h^3\cdot h$ , and h^3(h+3)=h^4+3h^3 . Subtracting from the numerator gives a remainder of -3h^3+h^2-2

$-3h^3=-3h^2\cdot h$ , and -3h^2(h+3)=-3h^3-9h^2 . Subtracting from the previous remainder gives a new remainder of 10h^2-2 .

$10h^2=10h\cdot h$ , and 10h(h+3)=10h^2+30h . Subtracting from the previous remainder gives a new remainder of -30h-2 .

$-30h=-30\cdot h$ , and -30(h+3)=-30h-90 . Subtracting from the previous remainder gives a new remainder of , which doesn't contain factors of , so we're done.

This means we have

$\dfrac{h^4+h^2-2}{h+3}=h^3-3h^2+10h-30+\dfrac{88}{h+3}$

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Find the remainder of (h^4+h^2-2)/(h+3)

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