Given the following expression:
[tex](2x-1)(x^2\text{ - 2) - x(}x^2\text{ - x - 2)}[/tex]
To be able to find the value of the constants a, b, c, and d, we must first simplify the expression in the form of ax^3 + bx^2 + cx + d.
We get,
[tex](2x-1)(x^2\text{ - 2) - x(}x^2\text{ - x - 2)}[/tex][tex]\text{ (2x}^3-4x-x^2+2)-(x^3-x^2\text{ - 2)}[/tex][tex]\text{ 2x}^3-4x-x^2+2-x^3+x^2+2=2x^3-x^3-x^2+x^2\text{ - 4x + 2 + 2}[/tex][tex]\text{ = x}^3+0x^2\text{ - 4x + 4}[/tex]
Therefore, (2x - 1)(x^2- 2) - x(x^2 - x - 2) when simplified is x^3 + 0x^2 - 4x + 4.
Following the standard form ax^3 + bx^2 + cx + d, the following constants are:
ax^3 = x^3 = 1x^3
a = 1
bx^2 = 0x^2
b = 0
cx = - 4x
c = -4
d = 4
In Summary: a = 1, b = 0, c = -4 and d = 4
