SOLUTION: use synthetic division to determine the answer. 7. Which one of the following numbers is a zero of the polynomial x^3 + 3x - 4? -2 -1 0 1 3 7

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Question 1206606: use synthetic division to determine the answer.
7. Which one of the following numbers is a zero of the polynomial x^3 + 3x - 4?
-2
-1
0
1
3
7
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39621)   (Show Source): You can put this solution on YOUR website!
Rational Roots Theorem tells you which possible roots to test. Then using synthetic division is simply a routine process.

The possible roots to test are -1, -2, -4, 1, 2, 4.


For sure, +1.
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


Note that synthetic division is a slow way to find which one of the answer choices is a root of the given polynomial; evaluating the polynomial for each of the answer choices is much faster.

However, the problem is possibly intended as practice with the process of synthetic division; so let's go ahead with it.

To start with, the rational roots theorem tells us the possible rational roots are 1, 2, 4, -1, -2, and -4. Of those, -2, -1, and 1 are answer choices.

With only a little experience with synthetic division, we know that trying 1 as a root makes for the easiest calculations, so we would try that answer choice first.

But, assuming the problem is to give us practice using synthetic division, let's try the valid answer choices in the order they are given.
trying -2 as a root....

   -2 |  1  0  3 -4
      |    -2  4 -14
      +-------------
         1 -2  7 -18  the remainder is not 0; -2 is not a root

trying -1....

   -1 |  1  0  3 -4
      |    -1  1 -4
      +-------------
         1 -1  4 -8  the remainder is not 0; -2 is not a root

trying 1....

    1 |  1  0  3 -4
      |     1  1  4
      +-------------
         1  1  4  0  the remainder is 0; 1 is a root

ANSWER: 1
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