Question

If ( x+2 ) is a factor of 2x^3+5x^2-x-k, find the value of K

Answer 1

Step-by-step explanation:

(x+2)=0x=-2

p(x)=2x^3+5x^2-x-k

p(-2)=2(-2)^3+5(-2)^2-(-2)-k=0

= -16+20+2-k=0

= 6-k=0

= -k= -6

on canceling minus sign on both sides we get:

= k=6 ANS.

I think u Understand the answer.

Answer 2

$\sf\huge\underline{Solution :-}$

If (x + 2) is a factor of the polynomial 2x³ + 5x² - x - k, find the value of k.

= Let's find the zero of the polynomial (x + 2),

=> x + 2 = 0

.°. x = -2

Putting the value of x in the polynomial,

=> 2 × (-2)³ + 5 × (-2)² - (-2) - k = 0

[Since, (x + 2) is a factor of the given polynomial.]

=> 2 × (-8) + 5 × 4 + 2 - k = 0

=> -16 + 20 + 2 - k = 0

=> - 16 + 22 - k = 0

=> 6 - k = 0

=> - k = - 6

.°. k = 6

Hence, the value of k is 6 when (x + 2) is a factor of 2x³ + 5x² - x - k respectively.