Question

The polynomial (in x) :
(x)6
+ 18(x)3+125, admits-


(A) No factor of degree
between 2 and 5
(B) x2–3x + 5 as a factor

(C) x + 1 as a factor
(D) x – 125 as a factor​

Answer 1

ANSWER

We solve the question by assuming option (B) to be true and then checking if it is true or not.

Assuming (B) to be true,

x

2

=3x−5

Substituting this,we get

x

6

+18x

3

+125

=(3x−5)

3

+18x(3x−5)+125

27x

3

−125−45x(3x−5)+54x

2

−90x+125

27x

3

−135x

2

+225x+54x

2

−90x

=27x

3

−81x

2

+135x

=27x(x

2

−3x+5)

=27x(3x−5−3x+5)

=0

Therefore, our assumption is correct.

Hence x

2

−3x+5 is factor.