Question

division algorithm,
6. Verify the following:
(1) (x - 11) is a factor of x2 - 8x - 33,​

Answer 1

Verification by division algorithm

____________

x - 11 ) x^2 - 8x - 33 ( x + 3

x^2 - 11x

- +

____________

3 x - 33

3 x - 33

- +

______________

0

Since,

the remainder on division is zer0

therefore,

it is verified that

x- 11 is a Factor of x^2 - 8x - 33 .

Verification by putting x = 11 as a root of given quadratic polynomial

we have

x^2 - 8x - 33

putting x = 11

( 11)^2 - 8 (11) -33

121 - 88 -33

121 - 121

= 0

Hence, verified.