When the expression $2x^3 + ax^2 -5x -2$ is divided by $2x-1$ , the remainder is $-3.5$ . Determine the value of the constant $a$ . Can someone please help?

Question

When the expression $2x^3 + ax^2 -5x -2$ is divided by $2x-1$ , the remainder is $-3.5$ . Determine the value of the constant $a$ .

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Answer 1 · 2018-05-21T22:09:36

$a = 3$

The remainder theorem states that if $P(x)$ is divided by $x - a$ , then the remainder is given by $P(a)$ .

Therefore:

$2(1/2)^3 + a(1/2)^2 - 5(1/2) - 2 = -3.5$

A little bit of algebra lets us simplify to

$2(1/8) + a(1/4) - 5/2 = -1.5$

$1/4a = -3/2 + 5/2 - 1/4$

$4(1/4a) = 4(-3/2 + 5/2 - 1/4)$

$a = -6 + 10 - 1$

$a = 3$

Hopefully this helps1