Question

How do you evaluate $f(-3)$ given $f(x)=4{{x}^{3}}+{{x}^{2}}-5x?$

Answer 1

To evaluate the given polynomial equation $f(x)=4{{x}^{3}}+{{x}^{2}}-5x$, we need to substitute the given value of$x$in the given polynomial equation provided, and then we have to compute the following polynomial equation with the given value of $x$ and the final value we get is the solution of the above given problem and the solution goes as follows
$f(-3)=4{{(-3)}^{3}}+{{(-3)}^{2}}-5(-3)$
Here the given $x$ value that is to be substituted in the polynomial equation is $-3$,and the polynomial expression is $f(x)=4{{x}^{3}}+{{x}^{2}}-5x$.

Complete step by step solution:
By substituting $-3$in the polynomial equation the equation look as follows:
By evaluating the equation found by substituting the value of $x$i.e.$-3$
We come across the following calculation,
That is,${{(-3)}^{3}}=-27$
${{(-3)}^{2}}=9$.
Substituting this value in the polynomial equation we get
$f(-3)=4{{(-3)}^{3}}+{{(-3)}^{2}}-5(-3)$
$\Rightarrow$ $4\times (-27)+9-5\times (-3)$
By evaluating further,
$\Rightarrow$ $-108+9-(-15)$
$\Rightarrow$ $-108+9+15$
$\Rightarrow$ $-108+24$
$\Rightarrow$ $-84$
Hence, from the above, we have successfully evaluated the given polynomial equation $f(x)=4{{x}^{3}}+{{x}^{2}}-5x$by substituting the given value of $x$, that is $-3$and the solution we have found is $-84$.

Note: wWe can solve the given problem by the above method of substitution. Here, students may find difficulty in evaluating the exponent factor of a negative number as given in the above problem, one should be careful in assigning sign to the resulting value after evaluating the exponent part of the negative number. The student also may find difficulty in the adding after the evaluation of particular terms, one should be careful in that.