Question

If p(x)=x^4-2x^3+3x^2-ax+8 is divided by x+1, we get a remainder 10. Find a.

Answer 1

Given p(x) = x^4 - 2x^3 + 3x^2 - ax + 8.

By remainder theorem,

= > x + 1 = 0

= > x = -1.

Given that we get a remainder 10.

Now,

p(-1) = (-1)^4 - 2(-1)^3 + 3(-1)^2 - a(-1) + 8 = 10

= > 1 + 2 + 3 + a + 8 = 10

= > a + 14 = 10

= > a = -4.

Therefore, the value of a = -4.

Hope this helps!

Answer 2

X+1=0
X=-1
p(-1)=(-1)^4-2(-1)^3+3(-1)^2-a(-1)+8
Rem=1+2+3+a+8
10=14+a
10-14=a
-4=a
a=-4