The equation represented by the model is 3x²-4x+1=(3x-1)(x-1).
Given model represents a polynomial of the form ax²+bx and model is in figure.
Consider the given table.
The first row in the table represents first term of the polynomial.
In first row first three terms are variables and last term are constant.
Write all the terms of the first row in the form of sum.
+x+x+x-1=3x-1
The first column in the table represents second term of the polynomial.
In first column first term are variable and last term are constant.
Write all the terms of the first column in the form of sum.
+x-1=x-1
The product of first term of polynomial (3x-1) and second term of polynomial (x-1) is equal to the sum of all remaining terms in this table.
+x²+x²+x²-x-x-x-x+1=3x²-4x+1.
We can also check this by multiplying (3x-1) and (x-1) as
(3x-1)(x-1)=3x(x-1)-1(x-1)
(3x-1)(x-1)=3x(x)-3x(1)-1(x)+1(1)
(3x-1)(x-1)=3x²-3x-x+1
(3x-1)(x-1)=3x²-4x+1
Hence, the equation represented by the given model in the form of polynomial ax²+bx is (3x-1)(x-1)=3x²-4x+1.
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