Question

check whether polynomial x-1 is a factor of polynomial
x ki power 5 - 8x ki power 4 +19x-12​

Answer 1

(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

#LearnMore

Check whether the polynomial x + 5 is a factor of the polynomial x^3-4x^2+3x-15.verify by division algorithm