Question

please answer this question ​

Answer 1

Answer :-

Polynomial g(x) = x + √2 is a factor of polynomial f(x) = 2√2 x² + 5x + √2.

Step-by-step explanation :-

Given :

f(x) = 2√2 x² + 5x + √2

g(x) = x + √2

To find :

To prove that g(x) is a factor of f(x) using factor theorem.

Solution :

g(x) = x + √2

g(x) = 0

x + √2 = 0

x = -√2

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f(x) = 2√2 x² + 5x + √2

f(-√2) = 2√2(-√2)² + 5(-√2) + √2

4√2 - 5√2 + √2

4√2 - 3√2

0

∴ Polynomial g(x) = x + √2 is a factor of polynomial f(x) = 2√2 x² + 5x + √2.

Factor theorem :

When a polynomial f(a) is divided by (x - a) and remainder f(a) is equal to 0, then (x - a) becomes factor of f(z).

Remainder theorem :

When a polynomial f(x) is divided by (x - a), then the value of f(a) is the remainder.