Question

the polynomials x^3+2×+3​

Answer 1

The Remainder is same whne (x−3) divides (x

3

−px

2

+x+6) & (2x

3

−x

2

−(p+3)x−6)

∴ Using Remainder Theorem

R(3)=x

3

−px

2

+x+6

=3

3

−p(3

2

)+3+6

=27−9p+3

=36−9p

R(3)=2x

3

−x

2

−(p+3)x−6

=2(3

3

)−3

2

−(p+3)3−6

=2×27−9−3p−9−6

=54−24−3p

=30−3p

Remainder are same

∴36−9p=30−3p

36−30=−3p+9p

6=6p

1=p

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