Question

Consider the expression
x to the [m-1] + 3; where is a constant. What is the least integer value
of for which the given expression is a polynomial in one variable?
a. 0
b. 1
c. 2
d. 3

Answer 1

I hope this usefull of you

Answer 2

The least integer value of m for which the given expression is a polynomial in one variable is 2.

• (a) is incorrect

The variables of a polynomial CANNOT be negative.

For $x^{m-1} +3$, if m = 0, the expression will be

$x^{0-1} +3=x^{-1} +3$, which is incorrect.

• (b) is incorrect

This is because if m = 1, $x^{m-1} +3$ will be $x^{1-1} +3=x^{0} +3$, which is in fact a constant, not a variable.

A constant polynomial is of the form f(x) = c. If m = 1, the expression will be $x^{0} +3$ which can be written in the form 1 + 3, that is 4.

• (c) is correct

For m = 2, $x^{m-1} +3$

= $x^{2-1} +3=x^{1} +3$, which is a monomial.

So, the least integer value for which $x^{m-1} +3$ is a polynomial in one variable is 2.

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