factorise 1/(y^-5)=32
Answers
If a polynomial function has integer coefficients, then every rational zero will have the form
p
q
where
p
is a factor of the constant and
q
is a factor of the leading coefficient.
p
=
±
1
,
±
32
,
±
2
,
±
16
,
±
4
,
±
8
q
=
±
1
Find every combination of
±
p
q
. These are the possible roots of the polynomial function.
±
1
,
±
32
,
±
2
,
±
16
,
±
4
,
±
8
Substitute
2
and simplify the expression. In this case, the expression is equal to
0
so
2
is a root of the polynomial.
Tap for more steps...
0
Since
2
is a known root, divide the polynomial by
x
−
2
to find the quotient polynomial. This polynomial can then be used to find the remaining roots.
x
5
−
32
x
−
2
Divide
x
5
−
32
by
x
−
2
.
x
4
+
2
x
3
+
4
x
2
+
8
x
+
16
Write
x
5
−
32
as a set of factors.
(
x
−
2
)
(
x
4
+
2
x
3
+
4
x
2
+
8
x
+
16
)