2. The envelope below has a mailing label. L(x) = 6x + 5 W(x) = 6x + 5 M(x) = x +4 NOx) = x + 2 MR. AL GEBRA 123 INFINITY WAY POLYNOMIAL, XY 11235 a. Let A(x) = L(x).W(X) - M(x)•N(x). Find A(x).

A(x) = 35x² + 54x + 17

Step-by-step explanation:

Relation in the polynomials has been defined as,

A(x) = L(x).W(x) - M(x).N(x)

L(x) = (6x + 5)

W(x) = (6x + 5)

M(x) = (x + 4)

N(x) = (x + 2)

By substituting the polynomials in the expression,

A(x) = (6x + 5)(6x + 5) - (x + 4)(x + 2)

      = (6x + 5)² - (x + 4)(x + 2)

      = (36x² + 60x + 25) - (x + 4)(x + 2) [Since, (a + b)² = a² + 2ab + b²]

      = (36x² + 60x + 25) - [x(x + 2) + 4(x + 2)]

      = (36x² + 60x + 25) - [x² + 2x + 4x + 8]

      = (36x² + 60x + 25) - [x² + 6x + 8]

      = (36x² - x²) + (60x - 6x) + (25 - 8)

      = 35x² + 54x + 17

A(x) = 35x² + 54x + 17

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