SOLUTION: if 4x³ + 8x² - x - 2 = 0 then the value of (2x + 3) is given by

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Question 899325: if 4x³ + 8x² - x - 2 = 0 then the value
of (2x + 3) is given by
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The conclusion may be given by the evaluation according to any values assigned to x. The polynomial of the equation has no restrictions on x. The polynomial can accept any real number for x. 2x+3 can accept any real number for x.

You can try polynomial division to test if 2x+3 is a factor of the cubic polynomial. The result of the division will be 2x%5E2%2Bx-2%2B4%2F%282x%2B3%29; meaning the remainder is "4". This would be equivalent for checking the root for 2x%2B3=0
2x=-3
x=-3%2F2

What that means basically is that when x=-3%2F2, then 4x%5E3%2B8x%5E2-x-2=4.
(This is related to either Factor Theorem or Remainder Theorem).