SOLUTION: Consider the polynomial 2x^3+ax^2-3x-1,where a is a constant .When x=1,the value of the polynomial is 2. a)find the value of a b) find the value of the polynomial when x=2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Consider the polynomial 2x^3+ax^2-3x-1,where a is a constant .When x=1,the value of the polynomial is 2. a)find the value of a b) find the value of the polynomial when x=2      Log On


   

Question 1200410: Consider the polynomial 2x^3+ax^2-3x-1,where a is a constant .When x=1,the value of the polynomial is 2.
a)find the value of a
b) find the value of the polynomial when x=2
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

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: a = 4

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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: 25