Y = (x2 - 2x + 1) y = (x - 1)(x - 1)
Prove that the following functions are equivalent through algebraic and numerical proof

see below

Step-by-step explanation:

y = (x² - 2x + 1)

y = (x - 1)(x - 1)

First, recognize that the first equation is fully simplified/expanded already.

Now, we should solve for the second equation.

FOIL the expressions: first–outer–inner–last

(x - 1)(x - 1)

F: x²

O: -x

I: -x

L: 1

Combine these terms.

x² - x - x + 1

x² - 2x + 1

Notice that this equation is identical to our first equation. Therefore, the functions are equivalent.

Hope this helps!

there are no answer choices

step-by-step explanation:

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!