What are the equations of the asymptotes of the rational function? Please explain. f(x)=
2 answers:
to get the vertical asymptotes, we simply zero out the denominator and see what's the equation so let's do so
x + 7 = 0............. x = -7....... that's the vertical asymptote.
to get the horizontal asymptotes, there are 3 cases
if the denominator's degree is higher, or lower or the exactly the same as the degree of the numerator.
well, notice the rational, the degree of the numerator is just 1, 6x¹, and the degree of the denominator is also 1, 1x¹.
when that occurs, the horizontal asymptote occurrs at the fraction of their leading term coefficients.
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A factorization of is
.
- The maximum number of roots of a polynomial of degree
is
- For a polynomial with real coefficients, the roots can be real or complex.
- The complex roots of a polynomial with real coefficients always exist in a pair of conjugate numbers i.e., if
is a root, then
is also a root.
If the roots of the polynomial are
, then it can be factorized as
.
Here, we are to find a factorization of . Also, given that
and
are roots of the polynomial.
Since is a polynomial with real coefficients, so each complex root exists in a pair of conjugates.
Hence, and
are also roots of the given polynomial.
Thus, all the four roots of the polynomial , are:
.
So, the polynomial can be factorized as follows:
Therefore, a factorization of is
.
To know more about factorization, refer: brainly.com/question/25829061
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