We have to find the value of p in the given polynomial when divided by x−3 leave the same remainder using remainder theorem
ML Aggarwal Avichal Publication Factorisation chapter 6, question no 8(i)
Rajan@2021Guru
When divided by x−3 the polynomials x 3 −px 2 +x+6 and 2x 3 −x 2 −(p+3)x−6 leave the same remainder. Find the value of ′ p ′
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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