Question

What is the remainder obtained when the polynomial
P(x) = $x^7+9x^5+5x^3+x-1$
is divided by $x–1$ ?

• A. 15, 15
• B. 15, 0
• C. 0, 15
• D. 0, 0

Answer 1

The correct option is A

15, 15

As per remainder theorem, the remainder
obtained when the polynomial is divided
by $x-1$ will be same as the value of
the polynomial at $x=1$.
$P\left(1\right)=1^7+9\times {\left(1\right)}^5+5\times {\left(1\right)}^3+1-1=15$.
Thus remainder when
$x^7+9x^5+5x^3+x-1$
is divided by $x–1$ is 15.