What must be subtracted from (x+ + 2x - 2x² + 4x + 6) so that the result
is exactly divisible by (x2 + 2x - 3)?
Answers
Answer:
et p(x) = x^4 + 2x^3 - 2x^2 + 4x + 6
Let g(x) = x^2 + 2x - 3.
We need to divide f(x) by g(x).
x^2 + 1
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x^2 + 2x - 3) x^4 + 2x^3 - 2x^2 + 4x + 6
x^4 + 2x^3 - 3x^2
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x^2 + 4x + 6
x^2 + 2x - 3
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2x + 9.
Thus, the expression x^4 + 2x^3 - 2x^2 + 4x + 6 is exactly divisible by x^2 + 2x - 3 when 2x + 9 is subtracted from it.
Step-by-step explanation: