Kinda lost with this one
Given that
hx^3 - 12x^2 - x + 3=(2x-1) (2x+1) (x-k)
find the values of the constants k and h
don't even know where to start
start by expanding the right side.
then you have
hx^3 - 12x^2 - x + 3 = 4x^3 - 4kx^2 - x + k
By comparing "like" terms, h would be 4 and k would be 3
To find the values of the constants k and h in the equation hx^3 - 12x^2 - x + 3 = (2x-1) (2x+1) (x-k), you can start by expanding the right side of the equation.
(2x-1)(2x+1)(x-k) can be expanded using the distributive property as follows:
(2x-1)(2x+1)(x-k) = (4x^2 -1)(x-k)
Now, multiply (4x^2 -1) with (x-k):
(4x^2 - 1)(x - k) = 4x^3 - 4kx^2 - x + k
Now, you can compare this expanded expression with the original equation hx^3 - 12x^2 - x + 3. By comparing the "like" terms of both sides of the equation, you can determine the values of the constants h and k.
First, compare the coefficient of x^3:
The coefficient of x^3 on the left side is h.
The coefficient of x^3 on the right side is 4.
Therefore, h = 4.
Next, compare the coefficient of x^2:
The coefficient of x^2 on the left side is -12.
The coefficient of x^2 on the right side is -4k.
Therefore, -4k = -12, which implies k = 3.
So, the values of the constants k and h are k = 3 and h = 4.