Question

(8x³ – 1) ' (2x–1) Find the quotient and remainder.

Answer 1

$\rm\textsf \green {Solution }$

$\textsf\red { We know the, algebraic identity \\\\ a^{3}-b^{3}=(a-b)(a^{2}+ab+b^2)}$

Here ,

$\frac{8x^{3}-1^{3}}{(2x-1)}$

=$\frac{(2x)^{3}-1^{3}}{(2x-1)}$

= $\frac{(2x-1)\cdot[(2x)^{2}+2x+1^{2}]}{(2x-1)}$

= $4x^{2}+2x+1$

Therefore ,

Remainder= 0

Quotient = $4x^{2}+2x+1$

••••

Answer 2

therefore

$remainder = 0$

$quotient =4 {x}^{2} + 2x + 1$