Question

If polynomial (3x3 + ax2 + 3x +5) and (4x3+x2-2x+a) leave
same remainder when divided by (x-2), find value of a
" find remainder in each case​

Answer 1

Answer:

Let the given polynomials are p(x)=3x

3

+ax

2

+3x+5 and f(x)=4x

3

+x

2

−2x+a

According to question p(2)=f(2)

3(2)

3

+a(2)

2

+3(2)+5=4(2)

3

+(2)

2

−2(2)+a

⇒3×8+4a+6+5=32+4−4+a

⇒24+4a+11=32+a

⇒4a−a=32−35

⇒3a=−3

⇒a=−1

As the remainder is same, so p(2) or f(2) would be same when a=−1

p(2)=3(2)

3

+(−1)(2)

2

+3×2+5[∴a=−1]

=24−4+6+5

=35−4=31

Thus, a=−1 and p(2) or f(2)=31