Question

given f(x) = 3x^3-5x^2-10 and g(x)=x^3+5x- are two polynomials .if f(x) and g(x) both are divided by (x-2) then the obtained remainders are r1 and r2 respectively . the value of (r1+r2 -r1 r2) is​

Answer 1

Given:

f(x) = 3x³ - 5x² - 10,  g(x) = x³ + 5x - 3

Both f(x) and g(x) are divided by (x - 2)

To find:

The value of, r₁ + r₂ -  r₁ r₂

Solution:

f(x) = 3x³ – 5x² – 10

Dividing by x - 2, we get,

x = 2

remainder =  3(2)³ - 5(2)² - 10   = 24 - 20 - 10  = - 6

r₁ = -6

g(x) = x³+ 5x - 3

Dividing by x - 2, we get,

x = 2

remainder =   (2)³ - 5(2) - 3   = 8   - 10 - 3  = - 5

r₂ = - 5

Now consider,

r₁ + r₂ -  r₁ r₂

= -6  - 5 - (-6)(-5)

= -11  - 30

= - 41

∴ r₁ + r₂ -  r₁ r₂ = - 41