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.
The factors of x2 are x and x x times x plus 1 = x2 + x
(x2 - x + 1)(x2 + x + 1)
x4 +x2 =x2 (x2+1)
X2+3x+x+3=x(x+1)+3(x+1)=(x+3)(x+1)
x3 + 1 = x3 + x2 - x2 - x + x + 1 = x2(x + 1) - x(x + 1) +1(x + 1) = (x + 1)(x2 - 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.
x3 + 1 = (x + 1)(x2 - x + 1) The x + 1's cancel out, leaving x2 - x + 1
x3 + x2 - x - 1 = x2(x+1) - 1(x+1) =(x+1)(x2-1) = (x+1)(x+1)(x-1)
x2 + 7x + 6 = (x + 6) (x + 1)
x2 + 4x + 3 = (x + 1)(x + 3)