Question

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Answer 1

Correct question :-

Given f(x) = 2x³ - 3x² + 1 and g(x) = x³ + 5x - 3 are 2 polynomials. If f(x) and g(x) both are divided by (x - 2), then the obtained remainders are are r₁ and r₂ respectively. The value of (r₁r₂ - r₁ - r₂) is

Solution :-

Using reminder theorem,

(x - 2) = 0

→ x = 2

Substitute the value of x in both f(x) and g(x)

f(x) = 2x³ - 3x² + 1

f(2) = 2(2)³ - 3(2)² + 1

→ f(2) = 16 - 12 + 1

→ f(2) = 4 + 1

→ f(2) = 5

So, 5 is the remainder of f(x) = r₁

g(x) = x³ + 5x - 3

g(x) = (2)³ + 5(2) - 36

→ g(x) = 8 + 10 - 3

→ g(x) = 18 - 3

→ g(x) = 15

So, 15 is the remainder of g(x) = r₂

Now,

we need to find the value of (r₁r₂ - r₁ - r₂)

r₁r₂ - r₁ - r₂

= 5(15) - 5 - 15

= 75 - 5 - 15

= 75 - 20

= 55

∴ The answer is 55