Question

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Answer 1

Heya !!!



Given that,



(X + 2) is a factor of the given polynomial.





Therefore,




(X + 2) = 0



X = -2




P(X) = 4X⁴ + 2X³ - 3X² +8X +5A



P(-2) = 4 × (-2)⁴ + 2 × (-2)³ - 3 × (-2)² + 8 × -2 + 5A






=> 4 × 16 + 2 × -8 - 3 × 4 - 16 + 5A = 0






=> 64 - 16 - 12 - 16 + 5A = 0



=> 64 - 44 + 5A = 0




=> 5A = -20




=> A = -20/5





=> A = -4





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Answer 2

Given that (x + 2) is the factor,


So, x + 2 = 0

x = -2

××××××××××××××××××

Putting the value of x in the given equation :



4x⁴ + 2x³ - 3x² + 8x + 5a = 0

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

4(16) + 2(-8) -3(4) + 8(-2) + 5a = 0

64 - 16 - 12 - 16 + 5a = 0

64 - 44 + 5a = 0

20 + 5a = 0

5a = -20

$a = - \frac{20}{5} \\ \\ a = - 4$




I hope this will help you


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