on dividing the polynomial 4x^4-5x³-39x²-46x-2 by the polynomial g(x) the quotient is x²-3x-5 & the remainder is -5x +8.find g(x)
on dividing the polynomial 4x^4-5x³-39x²-46x-2 by the polynomial g(x) the quotient is x²-3x-5 & the remainder is -5x +8.find g(x)
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Dividend = (Divisor × quotient) + Remainder
Now substitute it in it.
4x⁴ - 5x³ - 39x² - 46x - 2 = [g(x) × (x² - 3x - 5)] + (-5x + 8)
4x⁴ - 5x³ - 39x² - 46x - 2 + 5x - 8 = g(x) × (x² - 3x - 5)
4x⁴ - 5x³ - 39x² - 41x - 10 = g(x) × (x² - 3x - 5)
g(x) = 4x⁴ - 5x³ - 39x² - 41x - 10 / (x² - 3x - 5)
After solving, the answer will be,
4x² + 7x + 2