Question

If the polynomial is $f(x) = 2{x^3} - 13{x^2} + 17x + 12$, find $f(2)$.

Answer 1

Hint: While solving such kinds of sum we need to substitute the value of x as 2 i.e., wherever there is x in the equation we need to substitute it by 2 and solve it without any calculation error.
BEDMAS stands for Brackets, Exponents, Division, Multiplication, Addition and Subtraction.

Complete step by step answer:
Given, $f(x) = 2{x^3} - 13{x^2} + 17x + 12$
Firstly, we will factorise the expression \[\]$2{x^3} - 13{x^2} + 17x + 12$
And in order to that we will first take x as common from the first three terms.
Thus, our expression becomes $x[2{x^2} - 13x + 17] + 12$ .
Now we will take x common from $2{x^2} - 13x$ to factorize further
Thus, our expression becomes $x[x(2x - 13) + 17] + 12$
$\therefore f(x) = x[x(2x - 13) + 17] + 12$ …… (1)
Now we can't say anything common from the above expression. So, we will now substitute x by 2 as we have to find $f(2)$
$\therefore f(2) = 2[2(2 \times 2 - 13) + 17] + 12$
Now we will first solve the round bracket as per BEDMAS rule. Inside the round bracket there are fundamental operations which are multiplication and subtraction. Among them we will first multiply and then subtract as per BODMAS rule
 $\therefore f(2) = 2[2(4 - 13) + 17] + 12$
$\therefore f(2) = 2[2( - 9) + 17] + 12$
Now we will find the product of 2 & -9
$\therefore f(2) = 2[ - 18 + 17] + 12$
Now we will solve the square bracket
$\therefore f(2) = 2[ - 1] + 12$
Now we will find the product of 2 and -1
$\therefore f(2) = - 2 + 12$
Finally, we will find the difference of 12 and 2 and will put the bigger number sign
$\therefore f(2) = 10$
Hence, the value of $f(2)$ is 10 if, $f(x) = 2{x^3} - 13{x^2} + 17x + 12$

Note:
Zeros of Polynomial: It is a solution to the polynomial equation, P(x) = 0. It is that value of x that makes the polynomial equal to zero
Factor of a polynomial: A non-zero polynomial g(x) is called a factor of any polynomial f(x) if and only if there exists some polynomial q(x) such that f(x) = g(x) q(x)
 If you don’t apply the BEDMAS rule while solving arithmetical parts in the sum then the answer will not be solved correctly.
Another approach to solve this sum would be by direct substitution
Given, $f(x) = 2{x^3} - 13{x^2} + 17x + 12$
Since, we have to find the value of $f(2)$, we will substitute the value of $x = 2$ in the given equation.
Therefore, the given equation becomes \[f(2) = 2 \times {2^3} - 13 \times {2^2} + 17 \times 2 + 12\] …… (1)
Solve the equation 1 by applying BODMAS rule
\[f(2) = 2 \times {2^3} - 13 \times {2^2} + 17 \times 2 + 12\]
We will first solve the exponent part.
$f(2) = 2 \times 8 - 13 \times 4 + 17 \times 2 + 12$
Now we will solve the multiplication part.
$f(2) = 16 - 52 + 34 + 12$
Now we will solve the additional part of the equation.
$f(2) = 62 - 52$
Now finally we will subtract and find the value of $f(2)$.
$f(2) = 10$
Hence, the value of $f(2)$ is 10 if $f(x) = 2{x^3} - 13{x^2} + 17x + 12$.