Question

Find the value of the polynomial $5x - 4{x^2} + 3$ at
(i) $x = 0$
(ii) $x = - 1$
(iii) $x = 2$

Answer 1

Hint: Substitute the value of the variable in the given expression to evaluate the value of the polynomial. Like in the first case for $x = 0$, substitute $x$ by $0$ in the given expression . The expression will then become a purely numerical expression devoid of any variables. So then calculate the value of this resulting expression.

Complete step-by-step answer:
Answer (i):
We put $x = 0$ in the given expression.
$ \Rightarrow 5x - 4{x^2} + 3$ $ = (5 \times 0) - (4 \times 0) + 3$ $ = 3$
So the value of the polynomial at $x = 0$ is $3$.
Answer (ii):
We put $x = - 1$ in the given expression.
$ \Rightarrow 5x - 4{x^2} + 3$
$ = (5 \times - 1) - \{ 4 \times {( - 1)^2}\} + 3$
$ = - 5 - (4 \times 1) + 3$
$ = - 5 - 4 + 3$
$ = - 9 + 3 = - 6$
So the value of the polynomial at $x = - 1$ is $ - 6$.
Answer (iii):
We put $x = 2$ in the given expression.
$ \Rightarrow 5x - 4{x^2} + 3$
$ = (5 \times 2) - \{ 4 \times {(2)^2}\} + 3$
$ = 10 - (4 \times 4) + 3$
$ = 10 - 16 + 3$
$ = 13 - 16 = - 3$
So the value of the polynomial at $x = 2$ is $ - 3$.

Note: While evaluating the expression, first substitute the variable with the value given in the question. Then sum up all the terms with the same sign first to avoid mistakes. We then arrive at the final answer. Make sure that you do not skip steps while calculating as that can lead to silly mistakes.