The expression above is an example of a polynomial. See the explanation below for how it works.
Polynomials are the sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer.
Let us use the following exercise.
Give an examples polynomials p(x),g(x),q(x) and r(x), which satisfy the division algorithm and (i) deg p(x)=deg q(x)
(i) deg p(x) = deg q(x)
Recall the formula
Dividend = Divisor x quotient + Remainder
p(x)=g(x)×q(x)+r(x)
When the divisor is constant, the degree of quotient equals the degree of dividend.
Let us assume the division of 4x² by 2.
Here, p(x)=4x²
g(x)=2
q(x)= 2x² and r(x)=0
Degree of p(x) and q(x) is the same i.e., 2.
Checking for division algorithm,
p(x)=g(x)×q(x)+r(x)
4x² =2(2x²2)
Hence, the division algorithm is satisfied.
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