Question

Plss answer ASAP!!
What must be added to a⁴+2a³+a-1 so that resulting polynomial is exactly divisible by a²+2a-3?
Thx in advance!

Answer 1

Let f = a^4 + 2a^3-2a^2+2a-3

The roots of a^2+2a-3 are -3,1. (or (x+3)(x-1) are factors of this equation)

By remainder theorem (x-a) is a factor of a function f, iff f(a) = 0

We need to show that (x+3) and (x-1) are also factors of a^4 + 2a^3-2a^2+2a-3. This can be shown by the above discussed remainder theorem.

It can be checked that f(1) = 0 and f(-3) = 0, Hence the a^2+2a-3 is a factor of a^4 + 2a^3-2a^2+2a-3.

Answer 2

Answer:

-5a+8 should be added so that it can be divisible.

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