Question

What are the quotient and remainder, when by x²+3x+1 , 3x⁴+5x³-7x²+2x+2 is divided?

Answer 1

Answer:

Quotient = 3x² - 4x + 2

Remainder = 0

Step-by-step explanation:

$3x^4+5x^3-7x^2+2x+2 \\ \\ 3x^4+9x^3-4x^3+3x^2-12x^2+2x^2-4x+6x+2 \\ \\ 3x^4+9x^3+3x^2-4x^3-12x^2-4x+2x^2+6x+2 \\ \\ 3x^2(x^2+3x+1)-4x(x^2+3x+1)+2(x^2+3x+1) \\ \\ (x^2+3x+1)(3x^2-4x+2)$

∴ The quotient is 3x² - 4x + 2 and the remainder is 0.

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