Divide first polynomial by second polynomial and write the answer in the form ‘Dividend = Divisor $\times$ Quotient + Remainder’.

(i) $x^{3} - 64; x - 4$ (ii) $5 x^{5} + 4 x^{4} - 3 x^{3} + 2 x^{2} + 2; x^{2} - x$

Open in App

Solution

(i)
$x^{3} - 64 = x^{3} + 0 x^{2} + 0 x - 64$

Using long division method,

Dividend = Divisor × Quotient + Remainder

$∴ x^{3} - 64 = (x - 4) \times (x^{2} + 4 x + 16) + 0$

(ii)
$5 x^{5} + 4 x^{4} - 3 x^{3} + 2 x^{2} + 2 = 5 x^{5} + 4 x^{4} - 3 x^{3} + 2 x^{2} + 0 x + 2$

Using long division method,

Dividend = Divisor × Quotient + Remainder

$∴ 5 x^{5} + 4 x^{4} - 3 x^{3} + 2 x^{2} + 2 = (x^{2} - x) \times (5 x^{3} + 9 x^{2} + 6 x + 8) + (8 x + 2)$

Suggest Corrections

Similar questions

=

\times

+

x^{3} - 64; x - 4

-

5 x^{5} + 4 x^{4} - 3 x^{3} + 2 x^{2} + 2

x^{2} - x

Join BYJU'S Learning Program