Question

Find the value of a, if x+2 is a factor of 4x⁴+2x³-3x²+8x+5a.

Answer 1

hope it will help you

Answer 2

Given : if x + 2 is a factor of 4x⁴ + 2x³ - 3x² + 8x + 5a.

 

Let, f (x) = 4x⁴ + 2x³ - 3x² + 8x + 5a

By factor theorem,  If (x + 2) is a factor of f(x) then f (- 2) = 0  :

⇒ 4 (- 2)⁴ + 2 (- 2)³ -  3 (-2)² + 8 (- 2) + 5a = 0

⇒ 4 × 16 + 2 × - 8  - 3 × 4 - 16 + 5a = 0

⇒ 64 - 16 - 12 - 16 + 5a = 0

⇒ 64 - 28 - 16 + 5a = 0

⇒ 36 - 16 + 5a = 0

⇒ 20 + 5a = 0

⇒ 5a = - 20

⇒ a = - 20/5

⇒ a = - 4

Hence, (x + 2) is a factor f (x) when a = - 4.

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