The product of −x2+5x−1 and a monomial is 4x2−20x+4.

What is the monomial?

M(x) = -4*x^0 = -4

Step-by-step 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

yes

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step-by-step explanation:

1/4 because there is 4 grades.