Question

X + 2 is a factor of polynomial x cube + x square + X - 2 and the remainder 4 is obtained by dividing this polynomial by x minus 2 find the value of a and b

Answer 1

Answer:

The value of a is - 0.25 and b is  0.5

Step-by-step explanation:

Given as :

A polynomial is  ax³ + bx² + x - 2

x + 2 is a factor of this polynomial with remainder = o

And x - 2 is another  factor of this polynomial with remainder = 4

i.e p(x) = ax³ + bx² + x - 2

   g(x) = x + 2       ,  r = 0

   h(x) = x - 2        , r = 2

Now, satisfy the values

i.e  g( - 2) =  a(-2)³ + b(-2)² + (-2) - 2

Or, g(-2) = - 8 a + 4 b - 4                    ..........A

Again

g( 2) =  a(2)³ + b(2)² + (2) - 2

Or, g(2) = 8 a + 4 b + 0                     ...........B

Solving eq A and eq B

i.e ( - 8 a + 4 b - 4 ) + ( 8 a + 4 b ) = 0

Or, ( - 8 a + 8 a) + ( 4 b + 4 b) = 4

Or, 0 + 8 b = 4

∴   b = $\dfrac{4}{8}$

i.e b = 0.5

Now, put the value of a in eq B

∵   8 a + 4 b = 0

So, 8 a = - 4 × 0.5

Or, 8 a = - 2

∴    a = $\dfrac{-2}{8}$

i.e a = - 0.25

Hence, The value of a is - 0.25 and b is  0.5 Answer