The other two zeroes of the
polynomial x² - 8x² +19x-12 if its
one zeroes is x=1 are
Answers
Answer:We have the polynomial
p
(
x
)
=
x
3
−
8
x
2
+
19
x
−
12
As the degree of the polynomial is greater than 2, we need to use Synthetic Division to factorize it.
In Synthetic Division, we first find a value of
x
that makes this polynomial equal to zero. That is, we need to find the ZERO of the polynomial. We do that by Trial and Error.
For
x
=
1
, this Polynomial will equal zero.
p
(
1
)
=
1
3
−
8
⋅
1
2
+
19
⋅
1
−
12
=
1
−
8
+
19
−
12
=
0
As
x
=
1
makes this polynomial zero, we know for sure that
(
x
−
1
)
is one of the factors of the polynomial.
To find the other two factors, we use the process of Synthetic Division. To explain the entire process of Synthetic Division using text is a bit difficult, but this image should help:
enter image source here
The 1, -7 and 12 give us another factor of the polynomial:
)
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