Question

if X + K is the gcd of x 2 - 2 x, - 15 and x 3 + 27 find the value of k

Answer 1

gcd means...........??

Answer 2

Answer:

K = 3

Step-by-step explanation:

Given : X + K is the gcd of$x^2 - 2 x-15$ and $x^3 + 27$

To Find :find the value of k

Solution:

Factorize $x^2-2x-15$

$x^2-2x-15$

$x^2-5x+ 3x-15$

$x(x-5) + 3(x- 5)$

$(x-5)(x+3)$

Factorize $x^3 + 27$

$x^3+ 27$

$(x)^3+ (3)^3$

$(x+3)(x^2-3x+ 9)$

So, GCD of $x^2-2x-15$ and $x^3 + 27$ is x+3

we are given that GCD = x+k

So, On comparing

x+K=x+3

K = 3

Hence the value of K is 3