Question

If (x + 2) is a factor of x3 − 6x2 + kx + 10, k equals

Answer 1

Answer:

$\boxed{\sf \ \ \ k=-11 \ \ \ }$

Step-by-step explanation:

for a given k we got

$x^3-6x^2+kx+10$

and we are looking for k so that

$x^3-6x^2+kx+10 = (x+2)(ax^2+bx+c)$

let s estimate

$(x+2)(ax^2+bx+c) = ax^3+bx^2+cx+2ax^2+2bx+2c\\\\= ax^3+(b+2a)x^2+(2b+c)x+2c$

we can identify the terms do

terms in $x^3$

   1 = a

terms in $x^2$

   -6=b+2a

terms in x

   k=2b+c

constant term

   10 = 2c

it gives c = 10/2=5 and as a=1 b = -6-2a=-6-2=-8

so k = -2*8+5=-16+5=-11

the answer is k=-11

and then

$x^3-6x^2-11x+10 = (x+2)(x^2-8x+5)$