Question

The polynomials $p\left(x\right)=k{x}^3+3x^2-3$ and $Q\left(x\right)=2x^3-5x+k$, when divided by (x - 4) leave the same remainder. The value of K is

• A. $2$
• B. $1$
• C. $0$
• D. $-1$

Answer 1

Answer: (B)

$1$

Given polynomials are $p\left(x\right)=k{x}^3+3x^2-3$ and $Q\left(x\right)=2x^3-5x+k$.

It is also given that these two polynomials leave the same remainder when divided by $(x-4)$, therefore, we equate the polynomials and substitute $x=4$ as shown below:

$k(4{)}^3+3(4{)}^2-3=2(4{)}^3-5(4)+k\Rightarrow 64k+48-3=128-20+k\Rightarrow 64k+45=k+108\Rightarrow 64k-k=108-45\Rightarrow 63k=63\Rightarrow k=1$

Hence, $k=1$.