Question

Find the value of $P(2)$ where $P(x) = 4{x^3} - 7{x^2} + 4x + 7$.

Answer 1

Hint: First we will understand the polynomial and what does it consist of.
Then by substituting the value of x we will get the value required answer i.e. $P(2)$.

Complete step by step solution: Given data: $P(x) = 4{x^3} - 7{x^2} + 4x + 7$

A polynomial is a mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables having non-negative integral exponents.

And the single term polynomial is known as monomial or we can say that a polynomial is a summation of multiple monomials of different exponents of variables.

Either a monomial or a polynomial is always a continuous function and is always defined in R or we can say that either a monomial or a polynomial is defined for each value of x in real number.

We can find the value of the polynomial at any value of ‘x’ by substituting x with that value

Therefore substituting $x = 2$

 $ \Rightarrow P(2) = 4{(2)^3} - 7{(2)^2} + 4(2) + 7$

Simplifying the cube and the square

$ \Rightarrow P(2) = 4(8) - 7(4) + 8 + 7$

$ \Rightarrow P(2) = 32 - 28 + 8 + 7$

Now, adding the terms

$ \Rightarrow P(2) = 19$

Note: We can also plot the graph of any polynomial by plotting the polynomial function in the y-axis
Where the graph of the given polynomial function will be