putting polynomials in standard form.
(x-3)^2(x-1)
To put a polynomial in standard form, we need to expand and simplify it.
Let's start by expanding the given polynomial, (x-3)^2(x-1):
First, apply the exponent to the binomial (x-3)^2:
(x-3)^2 = (x-3)(x-3) = x(x-3) - 3(x-3) = x^2 - 3x - 3x + 9
= x^2 - 6x + 9
Now, multiply the result by (x-1):
(x^2 - 6x + 9)(x-1) = x^2(x-1) - 6x(x-1) + 9(x-1)
= x^3 - x^2 - 6x^2 + 6x + 9x - 9
= x^3 - 7x^2 + 15x - 9
So, the expanded form of (x-3)^2(x-1) is x^3 - 7x^2 + 15x - 9.
Now we have our polynomial in the expanded form. To put it in the standard form, we need to arrange the terms in descending order of the exponent.
Therefore, the standard form of (x-3)^2(x-1) is:
x^3 - 7x^2 + 15x - 9