Answer: M(x) = -4*x^0 = -4
Explanation:
A monomial is a polynomial with only a term.
We can write a random monomial as:
M(x) = a*x^n
Where n is a natural number.
Then we know that:
(-x^2 + 5*x - 1)*a*x^n = 4*x^2 - 20*x + 4
Solving the left side, we get:
-a*x^(2 + n) + a*5*x^(1 + n) - a*1*x^n = 4*x^2 - 20*x + 4
First, we can see that the powers of x do not change after multiplying by the monomial, this means that we must have n = 0. Then we have:
-a*x^2 + a*5*x - a = 4*x^2 - 20*x + 4
The terms with equal powers of x must be equal between them, this means that:
-a*x^2 = 4*x^2
a*5*x = -20*x
-a = 4
From the last equation, (we also could get the same by solving the first or second) we get that a = -4
Then the monomial will be:
M(x) = -4*x^0 = -4