Question

The value of polynomial \[{\text{f(x) = 4}}{{\text{x}}^{\text{3}}}{\text{ + 3}}{{\text{x}}^{\text{2}}}{\text{ + 2x + x}}\] at \[{\text{x = 3}}\] is

Answer 1

Hint: Here we have to find out the value of the given polynomial at the particular point.
Also, we discuss the definition of Polynomials that are algebraic expressions that may comprise exponents which are added, subtracted, or multiplied.
Polynomials where the largest exponent on the variables is three are known as cubics.
So we can say that the cubic polynomial is a polynomial of degree equal to 3.
In this question, the cubic polynomial was given.
Applying the \[{\text{x}}\] value in a given cubic polynomial and simplifies properly.
Finally, we will get the required results.

Complete step-by-step solution:
It is given that the question stated as the polynomial is \[{\text{f(x) = 4}}{{\text{x}}^{\text{3}}}{\text{ + 3}}{{\text{x}}^{\text{2}}}{\text{ + 2x + x}}\]
Here we have to find out the value of \[{\text{f(x)}}\] at a point \[{\text{x = 3}}\]
Now we have to substitute the \[{\text{x}}\] value in given cubic polynomial and we can write it as,
\[\Rightarrow{\text{f(3)= 4(3}}{{\text{)}}^{\text{3}}}{\text{ + 3(3}}{{\text{)}}^{\text{2}}}{\text{ + 2(3) + 3}}\]
On cubic and square the bracket term and we get,
\[{\text{ = 4}} \times 27 + 3 \times 9 + 2\left( 3 \right) + 3\]
On multiply the terms and we get,
\[ = 108 + 27 + 6 + 3\]
Let us add the term and we can write it as,
\[ \Rightarrow {\text{f(3) }} = 144\]
Hence, the cubic polynomial \[{\text{f(x) = 4}}{{\text{x}}^{\text{3}}}{\text{ + 3}}{{\text{x}}^{\text{2}}}{\text{ + 2x + x}}\] at the point \[{\text{x = 3}}\] is \[144\].

Therefore the value of the polynomial at x=3 is 144.

Note: In particular, for an expression to be a polynomial term, it must contain no fractional, negative powers on the variables or no square roots of variables and no variables in the denominators of any fractions.
Also, we remember that when we multiply two terms together, first we multiply the coefficient (numbers) and then add the exponent and finally combine like terms.