find the quotient and the remainder if the polynomial 4x^3+20x^2+33x+18
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Step-by-step explanation:
4x^3 +20x^2 +33x + 18
=> 4x^3 +8x^2 +12x^2 + 24x + 9x + 18
=> 4x^2 (x+2) + 12x(x+2) + 9(x+2)
=> (x+2)(4x^2 +12x +9)
=> (x+2)(4x^2 +6x + 6x +9)
=> (x+2)[2x(2x+3) + 3(2x+3)]
=> (x+2)(2x+3)(2x+3)
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