Question

Given f(x) = 3x3 – 5x2 – 10 and g(x) = x3 + 5x – 3 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 – r1r2) is

Answer 1

Given : f(x) = 3x³ – 5x² – 10  ,  g(x) = x³+ 5x – 3 both are divided by (x –2), then the obtained remainders are  r₁  & r₂

To find : r₁ + r₂ -  r₁ r₂

Solution:

f(x) = 3x³ – 5x² – 10

Divided by x - 2  => x = 2

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

r₁ = -6

g(x) = x³+ 5x – 3

Divided by x - 2  => x = 2

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

r₂ = - 5

r₁ + r₂ -  r₁ r₂

= -6  - 5 - (-6)(-5)

= -11  - 30

= - 41

r₁ + r₂ -  r₁ r₂ = - 41

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Answer 2

r₁ + r₂ -  r₁ r₂  = - 41

Step-by-step explanation:

Given: f(x) = 3x³ – 5x² – 10

g(x) = x³+ 5x – 3

Both are divided by (x –2), and the remainders are  r₁  & r₂.

Find: r₁ + r₂ -  r₁ r₂

Solution:

f(x) = 3x³ – 5x² – 10

f(x) / (x-2) = 3x³ – 5x² – 10 / (x-2)

Substituting x = 2, we get:

So r₁ = 3(2)³ – 5(2)² – 10

r₁ = 24  - 20 - 10

r₁ = - 6

g(x) = x³+ 5x – 3

Substituting x = 2, we get:

So r₂ = (2)³ – 5(2)  – 3

r₂   = 8   - 10 - 3

r₂  = - 5

Therefore, r₁ + r₂ -  r₁ r₂ = -6  - 5 - (-6)(-5)

 = -11  - 30

 = - 41