Question

Divide the polynomial by the binomial. Write your answer in the form: Dividend = divisor × quotient + remainder

(4) b⁴ – 12b²; b² + 1

Answer 1

(b⁴ – 12b²) ÷ ( b² + 1 ) can be shown as:

$$\begin{gathered} b^2-13 \\ {b}^2+1\overline{)b^4-12b^2} \\ {b}^4+b^2 \\ \underline{--} \\ 0-13b^2 \\ -13b^2-13 \\ \underline{++} \\ \underline{+13} \end{gathered}$$

Dividend = divisor × quotient + remainder
$\therefore b^4-12b^2=(b^2+1)\left(b^2-13\right)+13$