80x^4 - 60x^3 - 60x^2 - 45x
5x(16x^3-12x^2-12x-9)
5x(2x-3)(8x^2+6x+3)
the discriminant of the quadratic is negative, so it has no real factors.
80x^4 - 60x^3 - 60x^2 - 45x
This one looks more promising.
= 5x(16x^3 - 12x^2 - 12x - 9)
let f(x) = 16x^3 - 12x^2 - 12x - 9
f(±1) ≠ 0
f(±3) ≠ 0
tried ±3/2, ±3/4, ±3/8, ±3/16
found f(3/2) = 16(27/8) - 12(9/4) - 12(3/2) - 9
= 54 - 27 - 18 - 9 = 0
so 2x-3 is a factor
Using long division divide 16x^3 - 12x^2 - 12x - 9 by 2x-3 and you should have an exact division
let me know what you got
The given expression is 80x^4 - 60x^3 - 60x^2 - 45x.
To understand this expression, let's break it down term by term:
- The first term is 80x^4. This means we have 80 times x raised to the power of 4.
- The second term is -60x^3. Here, we have -60 times x raised to the power of 3.
- The third term is -60x^2, which means we have -60 times x raised to the power of 2.
- The last term is -45x, indicating we have -45 times x.
To simplify this expression, we can combine like terms. Like terms are terms that have the same variable raised to the same power:
Combine the terms:
80x^4 - 60x^3 - 60x^2 - 45x
To combine the terms, we add or subtract their coefficients (the numbers in front of the variable) while keeping the variable term the same.
In this case, there are no like terms we can combine because the variables have different powers. Thus, the expression cannot be further simplified.
Therefore, the simplified form of the given expression is 80x^4 - 60x^3 - 60x^2 - 45x.