It is a polynomial of the fourth degree in X.
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The factors of x2 are x and x x times x plus 1 = x2 + x
X2+3x+x+3=x(x+1)+3(x+1)=(x+3)(x+1)
(x4 - 2x3 + 2x2 + x + 4) / (x2 + x + 1)You can work this out using long division:x2 - 3x + 4___________________________x2 + x + 1 ) x4 - 2x3 + 2x2 + x + 4x4 + x3 + x2-3x3 + x2 + x-3x3 - 3x2 - 3x4x2 + 4x + 44x2 + 4x + 40R∴ x4 - 2x3 + 2x2 + x + 4 = (x2 + x + 1)(x2 - 3x + 4)
(X + 5)(X + 1) FOIL this. X2 + 1X + 5X + 5 Gather terms. X2 + 6X + 5 ----------------------------those were the factors
x² + x² is written as x²(1 + 1). Then, 1 + 1 = 2. Therefore, the answer is 2x².