Divide $6 x^{2} - 31 x + 47$ by $2 x - 5$ and verify the division algorithm.

Open in App

Solution

Let, $p (x) = 6 x^{2} - 31 x + 47$ ,
$g (x) = 2 x - 5$
$q (x) = 3 x - 8$
and $r = 7$

$∴$ By division algorithm,

$p (x) = g (x) \times q (x) + r$
$= (2 x - 5) (3 x - 8) + 7$
$= 6 x^{2} - 15 x - 16 x + 40 + 7$
$= 6 x^{2} - 31 x + 47$
$= p (x)$

Hence division algorithm is verified.

Suggest Corrections

Similar questions

x^{3} - 6 x^{2} + 11 x - 6

x - 2

Write the quotient and remainder when we divide.

$(6 x^{2} - 31 x + 47) b y (2 x - 5)$

Divide $2 x^{2} + x - 15$ by $x + 3$ and verify the division algorithm.

(6 x^{2} - 31 x + 47)

(2 x - 5)

2 x^{2} + 3 x + 1

(x - 2)

= 15

= 2 x + 7

Join BYJU'S Learning Program