Question

If the expression 2

6x²+13x+k is divisible by 2x+3, then what is the factor of the

expression?​

Answer 1

Answer:

[3x+2] and [2x+3] are the factors of the given polynomial

Step-by-step explanation:

Here if the polynomial is divisible by any other polynomial then the remainder must be zero when the value of x {i.e., 2x+3 } can be substituted then the whole value is equal to zero

ABOVE STATEMENT IS ALSO KNOWN AS REMAINDER THEOREM

here 2x+3=0 ⇒ x=-3/2 substitute in another polynomial

6(-3/2)²+13(-3/2)+k = 0

54/4 + (-39/2) + k =0

27/2 - 39/2 + k = 0

-12/2 + k = 0

-6 + k = 0

k = 6

the polynomial is 6x²+13x+6

2x+3 is also a factor of 6x²+13x+6

6x²+9x+4x+6=0

3x(2x+3)+2(2x+3)=0

(3x+2)(2x+3)=0

[3x+2] and [2x+3] are the factors of the given polynomial

PLEASE MARK THIS ANSWER AS THE BRAINLIEST ANSWER