Question

The remainder when f(x) = 4x³ – 3x² + 2x – 1 is divided by 2x + 1 is __________.

Answer 1

Let f(x) = 4x³ – 3x² + 2x – 1

To find the remainder obtained when 4x³ – 3x² + 2x – 1 is divided by 2x + 1,

we use remainder theorem, put 2x + 1 = 0.

f($-\frac{1}{2}$) is the remainder.

Now,

$$\begin{gathered} f\left(-\frac{1}{2}\right)=4{\left(-\frac{1}{2}\right)}^3-3{\left(-\frac{1}{2}\right)}^2+2\left(-\frac{1}{2}\right)-1 \\ =4\left(-\frac{1}{8}\right)-3\left(\frac{1}{4}\right)-1-1 \\ =-\frac{1}{2}-\frac{3}{4}-2 \\ =\frac{-2-3-8}{4} \\ =-\frac{13}{4} \end{gathered}$$

Hence, the remainder when f(x) = 4x³ – 3x² + 2x – 1 is divided by 2x + 1 is $\underline{-\frac{13}{4}}.$