Question 1200410
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Part (a)


Plug in x = 1 to get...
2x^3+ax^2-3x-1
2(1)^3+a(1)^2-3(1)-1
2(1)+a(1)-3(1)-1
2+a-3-1
a-2


We're told the polynomial output is 2 when x = 1
We'll set the a-2 equal to 2 and solve for 'a'
a-2 = 2
a = 2+2
a = 4


This means
2x^3+ax^2-3x-1
updates to
2x^3+4x^2-3x-1



Answer:  <font color=red>a = 4</font>


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Part (b)


Plug x = 2 into the polynomial we found earlier.
2x^3+4x^2-3x-1
2(2)^3+4(2)^2-3(2)-1
2(8)+4(4)-3(2)-1
16+16-6-1
32-6-1
26-1
25



Answer: <font color=red>25</font>
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