Question

Determine the value of a for
which the polynomial) 2x4- ax3+ 4x3 +2x +1 is divided by (1 -2x)

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Answer 1

Answer:

p(x) = 2x^4-ax³+4x²+2x+1

g(x) = 1-2x

1-2x = 0

-2x = -1

2x = 1

x = 1/2

p(1/2) = 2(1/2)^4-a(1/2)³+4(1/2)²+2(1/2)+1

= 2(1/16)-a(1/8)+4(1/4)+2(1/2)+1

= 1/8-a/8+1+1+1

= 1/8-a/8+3

= 1-a+24/8

= 25-a/8

(25-a) /8 = 0

25-a = 0

-a = -25

a = 25