Value of missing coefficient (a)

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The polynomial function q(x)= x^4+ax^3-19x^2-46x+120 has a root of -4. What is the value of the missing coefficient, a? Show your work and explain your reasoning.

May 4th, 2015

Raise x to the 2nd power

  x4-4x3-19x2+106x-120 
 ("Dividend")By :  x-4 ("Divisor")

dividend x4 - ax3 - 19x2 - 46x + 120 
- divisor * x3  x4 - 4x3 
remainder- ax2 - 46x + 120 
- divisor * 0x2 
remainder- ax2 - 46x + 120 
- divisor * -ax1 + ax2 + 19x 
remainder 30x + 120 
- divisor * 30x0  30x + 120 
remainder19

a = 19

May 4th, 2015

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