Question

When divided by x – 3 the polynomials x3 – px2 + x + 6 and 2x3 – x2 – (p + 3) x – 6 leave the same remainder. Find the value of ‘p’.​

Answer 1

1=p

Step-by-step explanation:

The Remainder is same whne (x−3) divides (x³−px²+x+6) & (2x³−x²−(p+3)x−6)

∴ Using Remainder Theorem

R(3)=x³−px²+x+6

=3³−p(3²)+3+6

=27−9p+3

=36−9p

R(3)=2x³−x²−(p+3)x−6

=2(3³)−3²−(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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