That depends on whether or not 2x is a plus or a minus
(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).
The quotient works out as: x^2+2x+4 and there is a remainder of -3
If the original is 2x + 3x2 + 6 + 5x3, you should rearrange the terms in order of exponent:5x3 + 3x2 + 2x + 6
-3x2 + 16x + 12 = -3x2 + 18x - 2x + 12 = -3x*(x - 6) - 2(x - 6) = -(3x + 2)*(x - 6)
(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).
== == Suppose f(x) = x3 + 3x2 - 2x + 7 divisor is x + 1 = x - (-1); so rem = f(-1) = 11
(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).
x3+3x2+6x+1 divided by x+1 Quotient: x2+2x+4 Remaider: -3
(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)
__x2_-_x______________ 2x - 1 ) 2x3 - 3x2 + x + 5 2x3 - x2 --------- -2x2 + x -2x2 + x ------------ 0 + 5 = 5 So the answer is x2 - x with remainder of 5. Couldn't get it to format correctly, but hopefully you can read it to understand the work.
if you rearrange it, it becomes 4y + 8 = 3x2 -2x +1 4y = 3x2 -2x -7 y= (3x2 -2x -7)/4 which is a parabola
3x2 + 2x + 3 + x2 + x + 1 = 4x 2+ 3x + 4
The quotient works out as: x^2+2x+4 and there is a remainder of -3
If it is 3x2 + 4 = 2x + 4, then you can subtract 4 from both sides, and get 3x2 = 2x, and then x = 2/3
f(x) = 2x3-3x2+x+5 f(x) becomes f(0.5) because 2*0.5-1 = 0 f(0.5) = 2*(0.5)3-3*(0.5)2+0.5+5 = 5 So the remainder is 5
3x2 + 2x - 21 = (3x - 7) (x + 3)
2x+3x2 = x (2+3x)