A manufacturer of metal washers needs to determine the​ cross-sectional area of each washer. If the outer radius of the washer is R and the radius of the hole is​ r, express the area of the washer as a polynomial. Factor this polynomial completely.

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The c.s.a. is found by subtracting the area of the hole from the total area (including the hole):
[tex]c.s.a.=\pi R^{2}-\pi r^{2}[/tex]
Factorizing completely we get:
[tex]c.s.a.=\pi(R+r)(R-r)[/tex]

A=π(R+r)(R-r) is the factorization of the polynomial.

What is Polynomial?

Factoring a polynomial exists expressing the polynomial as a product of two or more factors; it stands somewhat like the reverse process of multiplying.

A polynomial exists as an expression consisting of indeterminates (also named variables) and coefficients, that concern only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

The hole in the washer will never contain an area because it does not occupy any surface of the object.

The area of any circle is[tex]$\pi r^{2}$[/tex].

To discover the area of this washer, take the area of the outer circle minus the area of the inner circle (the hole).

[tex]$A=\pi R^{2}-\pi r^{2}$[/tex]

[tex]$A=\pi\left(R^{2}-r^{2}\right)$[/tex]

The term [tex]$\left(R^{2}-r^{2}\right)$[/tex] is a difference in perfect squares.

[tex]$A=\pi(R+r)(R-r)$[/tex]

To learn more about Polynomial refer to:

https://brainly.com/question/1600696

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