Question

if (x-3) is a factor of the polynomial (2x2+x+k). find k

Answer 1

If x - 3 is the factor of polynomial then when we put x as 3 then it will give 0 as resultant.

( 2x² + x + k ) = 0

2 × ( 3 )² + 3 + k = 0

2 × 9 + 3 + k = 0

18 + 3 + k = 0

21 + k = 0

k = - 21

Answer 2

Given:

(x-3) is a factor of the polynomial

$2 {x}^{2} + x + k$

To find:

The value of k.

Solution:

The value of k is -21.

To answer this question, we will follow the following steps:

First of all, we should know that if a polynomial p(x) has a factor (x - a), then x = a will satisfy the polynomial p(x). This means

p(a) = 0

or

'a' will be one of the zeroes of the polynomial.

Now, as given,

we have,

(x - 3) is a factor of the given polynomial-

$2 {x}^{2} + x + k$

So,

x = 3 will satisfy the given polynomial for which p(3) = 0

So,

On putting x = 3 in the given polynomial, we get

$2( {3)}^{2} + 3 + k = 0$

$21 + k = 0$

$k = - 21$

Hence, the value of k is -21.