check whether polynomial x-1 is a factor of polynomial
x ki power 5 - 8x ki power 4 +19x-12
Answers
(x-1) is a factor of polynomial p(x) = x^3-8x^2+19x-12p(x)=x
3
−8x
2
+19x−12
Step-by-step explanation:
We are given the following polynomial in the question:
p(x) = x^3-8x^2+19x-12p(x)=x
3
−8x
2
+19x−12
We have to check whether (x-1) is a factor of given polynomial or nor.
Put (x-1) = 0
\begin{gathered}x-1 =0\\x = 1\end{gathered}
x−1=0
x=1
Now, we check if x = 1 is a root of given polynomial or not.
Putting x = 1, we get,
\begin{gathered}p(1) = (1)^3-8(1)^2+19(1)-12\\p(1) = 0\end{gathered}
p(1)=(1)
3
−8(1)
2
+19(1)−12
p(1)=0
Thus, x = 1 is a root of the given polynomial.
Hence, (x-1) is a factor of polynomial p(x) = x^3-8x^2+19x-12p(x)=x
3
−8x
2
+19x−12
Division algorithm:
\begin{gathered}p(x) = x^3-8x^2+19x-12 = (x^2-7x+12)(x-1)\\p(x) = q(x) (x-1) + 0\\q(x) = x^2-7x + 12\end{gathered}
p(x)=x
3
−8x
2
+19x−12=(x
2
−7x+12)(x−1)
p(x)=q(x)(x−1)+0
q(x)=x
2
−7x+12
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