if you rearrange it, it becomes 4y + 8 = 3x2 -2x +1 4y = 3x2 -2x -7 y= (3x2 -2x -7)/4 which is a parabola
3x3 - 3x2 + 2x - 2 = 3x2(x - 1) + 2(x - 1) = (3x2 + 2)(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)
9x2 - 18x = -3x2 - 2x = -1/3x2 - 2x + 1 = 1 - 1/3(x - 1)2 = 2/3x - 1 = ±√2/3x = 1 ± (1/3)√6)
== == Suppose f(x) = x3 + 3x2 - 2x + 7 divisor is x + 1 = x - (-1); so rem = f(-1) = 11
3x3 - x2 - x - 1 = 3x3 - 3x2 + 2x2 - 2x + x - 1 = 3x2(x - 1) + 2x(x - 1) + 1(x - 1) = (3x2 + 2x + 1)(x - 1) So 3x3 - x2 - x - 1 /(x - 1) = (3x2 + 2x + 1)
if you rearrange it, it becomes 4y + 8 = 3x2 -2x +1 4y = 3x2 -2x -7 y= (3x2 -2x -7)/4 which is a parabola
It is: (3x+1)(x-1)
3x3 - 3x2 + 2x - 2 = 3x2(x - 1) + 2(x - 1) = (3x2 + 2)(x - 1)
(12x3 + 14x2 + 14x + 2)/(4x + 2) simplify= (6x3 + 7x2 + 7x + 1)/(2x + 1)1. 6x3 + 7x2 - 3x2(2x + 1) = 6x3 - 6x3 + 7x2 - 3x2 = 4x2; bring down 7x2. 4x2 + 7x - 2x(2x + 1) = 4x2 - 4x2 + 7x - 2x = 5x bring down 13. 5x + 1 - 2(2x + 1) = 5x - 4x + 1 - 2 = x - 1 the reminderThus, (6x3 + 7x2 + 7x + 1)/(2x + 1) = 3x2 + 2x + 2 + (x - 1)/(2x + 1)and(12x3 + 14x2 + 14x + 2)/(4x + 2) = 3x2 + 2x + 2 + (2x - 2)/(4x + 2).
(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)
3x2 + 2x + 3 + x2 + x + 1 = 4x 2+ 3x + 4
9x2 - 18x = -3x2 - 2x = -1/3x2 - 2x + 1 = 1 - 1/3(x - 1)2 = 2/3x - 1 = ±√2/3x = 1 ± (1/3)√6)
(3x4 + 2x3 - x2 - x - 6)/(x2 + 1)= 3x2 + 2x - 4 + (-3x - 2)/(x2 + 1)= 3x2 + 2x - 4 - (3x + 2)/(x2 + 1)where the quotient is 3x2 + 2x - 4 and the remainder is -(3x + 2).
== == Suppose f(x) = x3 + 3x2 - 2x + 7 divisor is x + 1 = x - (-1); so rem = f(-1) = 11
3x2 + 2x + 2 = 0 Can not be factored. You can however solve it for x: 3x2 + 2x = -2 x2 + 2x/3 = -2/3 x2 + 2x/3 + 1/9 = -2/3 + 1/9 (x + 1/9)2 = -5/9 x + 1/9 = ±√(-5/9) x = -1/9 ± i√(5/9) x = -1/9 ± i√5 / 3 x = -1/9 ± 3i√5 / 9 x = (-1 ± 3i√5) / 9
x2+8x = -3x2+5 4x2+8x-5 = 0 (2x+5)(2x-1) = 0 x = -5/2 or x = 1/2