Question
For what values of x is the following polynomial expression undefined? (x^2+4x+3)/(2x^2)-x-10ast (2x^2+4x^3)/(x^2)+3xdiv (x^2+3x+2)/(x) Select one or more: D a. -2 D b. -5/2 C. -1 D D d. -3 e. 0 f. 5/2 D g. 2 D D h. 3 D i. 1
Answer
3.7
(222 Votes)
Lucinda
Professional · Tutor for 6 years
Answer
To determine the values of
for which the given polynomial expression is undefined, we need to identify the values of
that would make any denominator in the expression equal to zero, since division by zero is undefined in mathematics.Let's analyze each denominator in the expression:1.
2.
3.
We will factor each of these to find their roots.1. For
, we look for two numbers that multiply to
and add up to
. These numbers are
and
. So we can factor the quadratic as:
The roots are
and
.2. For
, we can factor out an
:
The roots are
and
.3. The last denominator is simply
, which is zero when
.Now, let's consider the numerator
from the division part of the expression. We factor it to find removable discontinuities:
The roots are
and
.However, these roots from the numerator do not make the entire expression undefined; they would potentially be removable discontinuities if the same factors appeared in the denominators. In this case,
is a factor of the denominator
, so it is not a removable discontinuity but a value that makes the expression undefined.Combining all the roots from the denominators, the values of
that make the expression undefined are:a.
(from
)b.
(from
)c.
(from
)e.
(from
and
)The accurate answer is that the expression is undefined for
values:a.
b.
c.
e.