x ÷ 2x2 = 1/2x
(x3 + 3x2 - 2x + 7)/(x + 1) = x2 + 2x - 4 + 11/(x + 1)(multiply x + 1 by x2, and subtract the product from the dividend)1. x2(x + 1) = x3 + x22. (x3 + 3x2 - 2x + 7) - (x3 + x2) = x3 + 3x2 - 2x + 7 - x3 - x2 = 2x2 - 2x + 7(multiply x + 1 by 2x, and subtract the product from 2x2 - 2x + 7)1. 2x(x + 1) = 2x2 + 2x2. (2x2 - 2x + 7) - (2x2 + 2x) = 2x2 - 2x + 7 - 2x2 - 2x = -4x + 7(multiply x + 1 by -4, and subtract the product from -4x + 7)1. -4(x + 1) = -4x - 42. -4x + 7 - (-4x - 4) = -4x + 7 + 4x + 4 = 11(remainder)
(2x)2 times (2x)2 = 16x4 (2x2) times (2x2) = 4x4
4x4 + 1 = (2x2 - 2x + 1)(2x2 + 2x + 1)
2x2-4x+5 divided by x-1 Quotient: 2x-2 Remainder: 3
2x2 ÷ x = 2x
x ÷ 2x2 = 1/2x
2x2- 2x = 2x*(x - 1)
(x3 + 3x2 - 2x + 7)/(x + 1) = x2 + 2x - 4 + 11/(x + 1)(multiply x + 1 by x2, and subtract the product from the dividend)1. x2(x + 1) = x3 + x22. (x3 + 3x2 - 2x + 7) - (x3 + x2) = x3 + 3x2 - 2x + 7 - x3 - x2 = 2x2 - 2x + 7(multiply x + 1 by 2x, and subtract the product from 2x2 - 2x + 7)1. 2x(x + 1) = 2x2 + 2x2. (2x2 - 2x + 7) - (2x2 + 2x) = 2x2 - 2x + 7 - 2x2 - 2x = -4x + 7(multiply x + 1 by -4, and subtract the product from -4x + 7)1. -4(x + 1) = -4x - 42. -4x + 7 - (-4x - 4) = -4x + 7 + 4x + 4 = 11(remainder)
(2x)2 times (2x)2 = 16x4 (2x2) times (2x2) = 4x4
2x2(2x - 1)(2x + 1)(4x2 + 1)
2x2 + 2x = 2x(x+1)
4x4 + 1 = (2x2 - 2x + 1)(2x2 + 2x + 1)
2x2-4x+5 divided by x-1 Quotient: 2x-2 Remainder: 3
(-2x2 + x + 1) / (x - 1) = (-2x - 1)(x - 1)/(x - 1) = -2x - 1
-1
2x2 - 72 would be factored into (2x - 12)(x + 6) or (2x + 12)(x - 6) To double check, multiply each pair: (2x - 12)(x + 6) = 2x2 + 12x - 12x - 72 = 2x2 - 72 (2x + 12)(x - 6) = 2x2 - 12x + 12 x - 72 = 2x2 - 72