Question

Determine the value of k so that x+2 is a factor of x³ +10x² +23x +k
​

Answer 1

Answer :

We have,

• x + 2 is a factor of the expression x³ +10x² +23x +k.

So put x + 2 equal to 0

= x + 2 = 0

= x = - 2

Now,

• Put x = - 2 in the equation

= x³ +10x² +23x +k

= (-2)³ + 10 (-2)² + 23(-2) + k

= -8 + 10 × 4 + (-46) + k $\:$

= -8 + 40 - 46 + k

= 32 - 46 + k

= - 14 + k

So, the value of k

= - 14 + k = 0

= k = 14

____________________________