The polynomial within the numerator is 9x²+45x+54.
Given the denominator of the initial expression is [tex]\frac{?}{3x^2+15x+18}[/tex] and also the rational expression simplifies to three.
A mathematical expression which will be rewritten to a rational fraction, an algebraic fraction specified both the numerator and therefore the denominator are polynomials. and a polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Let's take the polynomial within the numerator is k.
So, rewrite the given expression as
[tex]\frac{k}{3x^2+15x+18}=3[/tex]
or it also can be written as
[tex]\frac{k}{3x^2+15x+18}=\frac{3}{1}[/tex]
Cross multiply either side as a×d=b×c where a=k, b=3x²+15x+18, c=3 and d=1 and acquire
k=3(3x²+15x+18)
Simplify the above expression,
k=9x²+45x+54
Hence, the polynomial within the numerator within the given expression [tex]\frac{?}{3x^2+15x+18}[/tex] which is simplified to 3 is 9x²+45x+54.
Learn about rational expression from here brainly.com/question/3764404
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