Question

find the L.C.M of the polynomial 12(x⁴-x³) and 8(x⁴-3x³+2x²)

Answer 1

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L.C.M of p(x), q(x) = x³ (x - 1) (x - 2)

Solution :

Given Polynomial

→ p(x) = 12 (x⁴- x³)

→ q(x) = (x⁴ - 3x³ + 2x²)

p(x) = 12(x⁴) (x³)

= 3 × 2 × 2 × x³ (x - 1)

q(x) = 12(x⁴ - 3x³ × 2x²)

⇒ x² (x² - 3x + 2)

⇒ x² (x² - x - 2x + 12)

⇒ x² (x - 1) (x - 2)

∴ L.C.M of p(x), q(x) = x³ (x - 1) (x - 2).

⇒ x² - 3x + 2 • a = 1, • b = 3, • c = 2.

⇒ a × b = 1 × 2 = 2.

⇒ x² - x - 2x + 2

⇒ (x - 1) = 2 (x - 1)

⇒ (x - 1) (x - 2).

Hope It'll Helps!