BBA-DBE Bangalore 2026 PYQsQuantitative Ability. Free, no login required.

Number System

Remainder

Medium

A polynomial $P(x)=x^4+3x^3-5x^2+7x+9$ is divided separately by $(x-2)$ and $(x+1)$ , giving remainders $R_1$ and $R_2$ , respectively. Find the value of $\dfrac{R_1+R_2}{2}$ .

✅ Correct Option: 1

By the Remainder Theorem, $R_1=P(2)$ and $R_2=P(-1)$ .

$P(2)=16+24-20+14+9=43$

$P(-1)=1-3-5-7+9=-5$

$\dfrac{R_1+R_2}{2}=\dfrac{43-5}{2}=19$ .

A polynomial P(x)=x4+3x3−5x2+7x+9P(x)=x^4+3x^3-5x^2+7x+9P(x)=x4+3x3−5x2+7x+9 is divided separately by (x−2)(x-2)(x−2) and (x+1)(x+1)(x+1), giving remainders R1R_1R1​ and R2R_2R2​, respectively. Find the value of R1+R22\dfrac{R_1+R_2}{2}2R1​+R2​​.