Question

For what value of a , x - 5 divide the polynomial x cube minus 3 X square + a x minus 10 exactly?

Answer 1

Given:

x - 5 divide the polynomial x cube minus 3 X square + a x - 10

To find :

The value of 'a' so that x-5 is a factor of the polynomial.

Solving Question:

We know the factor theorem it states that if 'a' is a factor of the polynomial p(x) then p(a) = 0

   By using this method we could find the answer. We could substitute the value of 'x'

Solution:

x - 5 = 0

or, x = 5

substitute this value in x³ - 3x² +ax - 10

⇒ (5)³ - 3(5)² + a*5 - 10 = 0 [as it is a factor ]

or, 125 - 75 +5a -10 = 0

or,  40 + 5a = 0

or, 5a = -40

or, a = -8

∴ The value of 'x' is -8

Answer 2

Answer:

See answer in attachment.