Question

check whether (x-2) is a factor of x3-2x2+3x-6
​

Answer 1

Answer:

yes,it is a factor

Step-by-step explanation:

x = 2

= 2×3 - 2×2 + 3×2 - 6

= 6 - 4 + 6 - 6

= 2 + 0

= 2

Answer 2

Solution:

Let,

→ f(x) = x³ - 2x² + 3x - 6

(x - 2) is a factor of f(x) if and only if f(2) = 0

So, putting x = 2, we get,

= (2)³ - 2 × (2)² + 3 × 2 - 6

= 8 - 8 + 6 - 6

= 0 + 0

= 0

So,

→ (x - 2) is a factor of f(x)

Answer:

• Yes, (x - 2) is a factor of the given polynomial.

Concept Used:

• Factor Theorem: If f(x) is a polynomial and α is a real number, then (x - α) is a factor of f(x) if and only if f(α) = 0.

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