3x2-4x-4=0 (3x+2)(x-2)+0 x=-3/2, 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= 6 6-(4x-2)= 6--8= 6+8 = 14 14+7 = 21
It is of the 2nd degree.
Given, 3x2 - 4x = -2 Then, 9x2 - 12x = -6; 9x2 - 12x + 4 = -2 {completing the square} ; 3x - 2 = ±i√2 {sq rt of both sides} ; and 3x = 2 ± i√2. Therefore, x = ⅓(2 ± i√2).
3x2-4x-4=0 (3x+2)(x-2)+0 x=-3/2, 2
x(3x-4)
3x2 + 4x factors to x(3x + 4)
3x2 + 2x - 8 = 3x2 + 6x - 4x - 8 = 3x(x + 2) - 4(x + 2) = (x + 2)(3x - 4).
x3 + 3x2 - 4x -12 x2(x + 3) - 4(x + 3) (x2 - 4)(x+3)
3x2 + 2x - 8 = 3x2 + 6x - 4x - 8 = 3x(x+2) - 4(x+2) = (3x-4)*(x+2)
The discriminant is -32.
no 3x2=6 then 4x-15= -60 so 6 added with - 60 = -54
3x2 + 4x + 1 = ?? This is a quadratic equation. The equation can be made to equal any number and this will determine the corresponding values of x. EXAMPLE : 3x2 + 4x + 1 = 96 (x = 5 or x = -19/3) Alternatively, if x is known then this will determine the result. EXAMPLE : If x = 2 then (3 x 4) + (4 x 2) + 1 = 12 + 8 + 1 = 21 In normal use, a quadratic equation is presented as equal to zero. In this example : 3x2 + 4x + 1 = 0
(3x+4)(x-2) 3x2 -6x+4x-8 3x2-2x-8
6x2 - 4x (6/2)x2 - (4/2)x = 3x2 - 2x ========
6x2 - 4x (6/2)x2 - (4/2)x = 3x2 - 2x ========