Question

find the value of gk if x+3 is a factor 3x²+kx+6​

Answer 1

Answer is in the photo attached check it out!!!!!!

Answer 2

Question:

Find the value of k if (x+3) is a factor of 3x² + kx + 6.

Answer:

k = 11

Note:

• Remainder theorem : If a polynomial p(x) is divided by (x - a) , then the remainder is p(a).

• Factor theorem : i) If (x-a) is a factor of polynomial p(x) , then the remainder obtained after dividing it by (x-a) is zero , ie ; p(a) = 0.

ii) If the remainder obtained after dividing a polynomial p(x) by (x-a) is zero , ie ; if p(a) = 0 , then (x-a) is a factor of polynomial p(x).

Solution:

Let the given polynomial be p(x) .

Thus,

p(x) = 3x² + kx + 6

Also,

It is given that , (x + 3) [can be written as {x - (-3)} ] is a factor of p(x).

Since,

{ x - (-3) } is a factor of polynomial p(x) , thus the remainder should be zero .

Thus,

=> p(-3) = 0

=> 3•(-3)² + k•(-3) + 6 = 0

=> 27 - 3k + 6 = 0

=> 33 - 3k = 0

=> 3(11 - k) = 0

=> 11 - k = 0

=> k = 11

Hence,

The required value of k is 3 .