Question

When
${x}^{2 } - 2x + k$
divides the polynomial
${x}^{4 } - 6 {x}^{3} + 16 {x}^{2} - 25x + 10$
the remainder is (x + a) . The value of k is _______​

Answer 1

Answer:

you're answer is given

Answer 2

k=5 & a=−5

x

2

−2x+k) x

4

−6x

3

+16x

2

−25x+10(x

2

−4x+(8−k)

−

x

4

+

−2x

3

−

+

kx

2

−4x

3

+(16−k)x

2

−25x+10

−

−4x

3

−

+8x

2

+

−

4kx

(8−k)x

2

+(4k−25)x+10

−

(

8−k)x

2

+

−

(

2k−16)x

−

+

(8k−k

2

)

(2k−9)x+(k

2

−8k+10)

But remainder is given x+a

∴x+a=(2k−9)x+(k

2

−8k+10)

On equating coefficient, we get

2k−9=1⇒k=5

and a=k

2

−8k+10⇒a=25−40+10=−5

Hence, k=5,a=−5

I hope it helps you