Question

6. The value of 'k' if 2x + x - 3x? - 26 leaves a
remainder of 226 when it is divided by x - 2 is:
(A)0
(B)5
(C)7
(D)9​

Answer 1

Answer:

f(x) = (x-a)q(x) +r

We can see that when we divide above polynomial by (x-a) it leaves remainder r. We find the value r simply by putting value of x=a. So,

f(a)=(a-a)q(a) +r

⟹

⟹

, r=f(a)

Let f(x) =  2+3−32−26

2

x

m

+

x

3

−

3

x

2

−

26

When we divide this by (x-2), it leaves remainder f(2).

f(2) =  2∗2+23−3∗22−262

∗

2m+23−3∗22−26

=  2+1+8−12−262m

1+8−12−26

=  2+1−30

2m+1−30

Which is given equal to 226.

2+1=256

2m+1=256

m+1 = 8

m = 7

Step-by-step explanation:

Answer 2

$\huge\frak\pink{answer}$

(2x−3) is a factor of p(x)=2x3−9x2+x+K,

If (2x−3)=0,x=23

If (2x−3) is a factor of p(x) then p(23)=0

p(x)=2x3−9x2+x+K,

⇒p(23)=2(23)−9(23)+23+K=0

⇒2(827)−9(49)+23+K=0

⇒(427−481+23+K=0

Hope this helps you✌☺