Question

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Answer 1

Answer:

(2x³ - 5x² + 4x - 3) is not a multiple of (x-2)

Step-by-step explanation:

Given that,

polynomial p(x) = 2x³ - 5x² + 4x - 3

multiple of p(x) i.e; g(x) = (x-2)

⇒ g(x) = (x-2) = 0 (let)

⇒ (x-2) = 0

⇒ x = 2

Now as x = 2, p(2) should be equal to '0' if p(x) is a multiple of g(x)

⇒ p(x) = 2x³ - 5x² + 4x - 3

⇒ p(2) = 2(2)³ - 5(2)² + 4(2) - 3

⇒ p(2) = 2(8) - 5(4) + 8 - 3

⇒ p(2) = 16 - 20 + 8 - 3

⇒ p(2) = 1 ≠ 0

∴ p(x) = 2x³ - 5x² + 4x - 3 is not a multiple of g(x) = (x-2)

HOPE THIS WOULD BE HELPFUL FOR YOU