6*x^3+15*x^2+16*x-2 This is done by substituting (x+1) for x in the original equation and expanding those factors.
no 3x2=6 then 4x-15= -60 so 6 added with - 60 = -54
(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).
3x2= 6 6-(4x-2)= 6--8= 6+8 = 14 14+7 = 21
The discriminant is -32.
They are: x = 5/3 and x = -3
It is: x = 5/3 and x = -3
2x4 - 9x3 + 13x2 - 15x + 9 = 2x4 - 6x3 - 3x3 + 9x2 + 4x2 - 12x - 3x + 9 = 2x3(x - 3) - 3x2(x - 3) + 4x(x - 3) - 3(x - 3) = (x - 3)*(2x3 - 3x2 + 4x - 3) So the quotient is (2x3 - 3x2 + 4x - 3) and the remainder is 0.
two complex
No real roots.
3x2 + 4x factors to x(3x + 4)
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
3x2-4x-15 = 0 (3x+5)(x-3) = 0 x = -5/3 or x = 3