Question

The polynomial q(z)=z^3 - 4z +a when divided by the polynomial (z- 3) leaves remainder 5. What is the value of a?​

Answer 1

Answer:

a = 10

Step-by-step explanation:

q(Z) = z³ - 4z + a

When divided by (z- 3) remainder is 5.

That means, for (z-3) to be a factor of q(z), q(z) should be 5 less than normal.

Therefore, (z-3) is a factor of q(z) - 5

q(z) - 5 = z³ - 4z + a - 5

Putting z = 3

q(3) - 5 = 3³ - 4 × 3 + a - 5

Using remainder theorem, such that if f(x) is divisible by (x - a), f(a) = 0.

0 = 27 - 12 + a - 5

0 = 10 + a

a = - 10

Hence, the value of a is 10

                                 

Hope this helps!