Question

What will be the quotient if $27x^3-81x^2+45x+23$ is divided by $(x–2)$?

• A. $27x^3-27x^2-9x-5$
• B. $27x^3-27x^2-9x+5$
• C. $27x^2-27x-9$
• D. $27x^2-27x+9$

Answer 1

The correct option is D $27x^2-27x+9$


Step 1 : We first write the coefficients of the dividend arranging them in descending powers of $x$ with zero as the coefficient of missing power of $x.$ Step 2 : To divide by $x-2,$ we write $x=2$.
Step 3 : Bring down the leading coefficient of the dividend, multiply it by $2$ and add the second coefficient to get $-27$.
Step 4 : Now, multiply $-27$ by $2$ and add this to the third coefficient to get $-9.$
Step 5 : This process is continued until the final sum.
Step 6 : Thus, we get the quotient as $27x^2-27x-9$ and the remainder as $5$.