Question

b) Find the value of k if (x-2) is a factor of x3 + 2x2 - kx + 10. Hence determine whether (x+5) is also a
factor.
​​

Answer 1

Answer:

k = -13

No x+5 is not a factor

steps

g(x) = x-2

let g(x) be = 0

then

0 = x-2

2=x

By remainder theorum we know that p(2) gives the remainder.

And it is given that x-2 is a factor.

Hence

p(2) = 2^3 + 2*2^2-2k+10

0 = 8+8-2k+10

0 = 26-2k

-26/2 = k

-13 = k

let f(x) = x+5

let f(x) = 0

then

0=5+x

x= -5

By remainder theorum we know that p(-5) gives the remainder.

If p(-5) = 0

then x+5 is a factor.

Else no.

Hope this helps

Answer 2

Answer:

Step-by-step explanation:

k = -13

No x+5 is not a factor

steps

g(x) = x-2

let g(x) be = 0

then

0 = x-2

2=x

By remainder theorum we know that p(2) gives the remainder.

And it is given that x-2 is a factor.

Hence

p(2) = 2^3 + 2*2^2-2k+10

0 = 8+8-2k+10

0 = 26-2k

-26/2 = k

-13 = k

let f(x) = x+5

let f(x) = 0

then

0=5+x

x= -5

By remainder theorum we know that p(-5) gives the remainder.

If p(-5) = 0

then x+5 is a factor.

Else no.

Hope this helps

Mark ab brainliest