Question

what must be added to f(x) = 4x⁴ + 2x³ - 2x² + x - 1 so that the resulting polynomial is divided by g(x) = x² + 2x - 3 ?
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Answer 1

Given:

p(x) = 4x⁴ + 2x³ - 2x² + x - 1

g(x) = x² - 2x - 3

Step-by-step explanation:

x² - 2x - 3)4x⁴ + 2x³ - 2x² + x - 1(4x² + 10x + 30

4x⁴ - 8x³ - 12x²

10x³ + 10x² + x - 1

10x³ - 20x² - 30x

30x² + 31x - 1

30x² - 60x - 90

91x + 89

∴ When the polynomial 91x + 89 is added to the polynomial 4x⁴ + 2x³ - 2x² + x - 1 then the added polynomial is completely divisible by x² - 2x - 3.

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Answer 2

answer: 4x^4 + 2x^3 - 3x^2 - x +2