Question

find reminder when 3x3-4x2+7x-5 is divided by (x-3) and (x+3)​

Answer 1

Solution:-

Polynomial f(x)= 3x³ - 4x + 7x - 5 divided by linear polynomial g(x) = (x - 3)

First we will find the zero of g(x)

=> (x - 3) = 0

=> x = 3

Therefore, The required remainder is f(3). Putting the value of x in f(x),

3x³ - 4x + 7x - 5

= 3.(3)³ - 4.3 + 7.3 - 5

= 3. 27 - 12 + 21 - 5

= 81 - 12 + 21 - 5

= 102 - 17

= 85

Hence, the remainder is 85 when the polynomial f(x)= 3x³ - 4x + 7x - 5

Hence, the remainder is 85 when the polynomial f(x)= 3x³ - 4x + 7x - 5is divided by g(x)= (x -3)

______________________________

Now,

Polynomial f(x)= 3x³ - 4x + 7x - 5 divided by linear polynomial g(x)= (x +3)

Zero of the polynomial g(x),

=> (x + 3) = 0

=> x = - 3

Therefore, the required remainder is f(-3). Now, Putting the value of x :-

3x³ - 4x + 7x - 5

= 3.(-3)³ - 4.(-3) + 7.(-3) - 5

= 3. (-27) - (-12) + (-21) - 5

= - 81 + 12 - 21 - 5

= -107 + 12

= -95

Hence, the remainder is -95 when the polynomial f(x)= 3x³ - 4x + 7x - 5

Hence, the remainder is -95 when the polynomial f(x)= 3x³ - 4x + 7x - 5is divided by g(x)= (x + 3)