Question

Fill in the blanks in the division –7b³ + 3b⁵ ÷ 3b³ shown below.

$$\begin{gathered} .......... \\ 3b^3\overline{)3b^5-7b^3} \\ .... \\ \underline{-} \\ -7b^3 \\ ....... \\ \underline{+} \\ ........ \end{gathered}$$

3b5 = 3b2 × ........ ∴ 3b5 ÷ 3b2 = .......... –7b3 = 3b3 × .......... ∴ –7b3 ÷ 3b3 = ........

Quotient: .........; Remainder : ...........
∴ 3b⁵ – 7b³ = (......) × (.........) + (.........)

Answer 1

$$\begin{gathered} b^2-\frac{7}{3} \\ 3b^3\overline{)3b^5-7b^3} \\ +3b^5 \\ \underline{-} \\ 0-7b^3 \\ -7b^3 \\ \underline{+} \\ \underline{0} \end{gathered}$$

3b5 = 3b2 × b3 ∴ 3b5 ÷ 3b3 = b2 –7b3 = 3b3 × $\underline{\left(\frac{-7}{3}\right)}$ ∴ –7b3 ÷ 3b3 = $\underline{\left(\frac{-7}{3}\right)}$

Quotient: $b^2-\frac{7}{3}$
Remainder: 0
Quotient = divisor × (quotient) + remainder
∴ 3b⁵ – 7b³ = (3b³) ×$\left(b^2-\frac{7}{3}\right)$ + (0)