SOLUTION: Someone please help me with this question. What are the factors of the polynomial function? Use the rational root theorem to determine the factors. {{{ f(x)= 2x^3 + x^2 -

Question 1127820: Someone please help me with this question.
What are the factors of the polynomial function?
Use the rational root theorem to determine the factors.

Select EACH correct answer.
A. (2x + 1)
B. (2x - 1)
C. (x + 2)
D. (x - 2)
E. (x - 1)
F. (x + 1)
G. (x - 4)
H. (x + 4)
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The rational roots theorem says that the possible rational roots for a polynomial are +/-(p/q), where p is a factor of the constant term and q is a factor of the leading coefficient. For this polynomial then, the possible roots are

+/- {1, 2, 4, 1/2}

When you find one root, you can divide the polynomial by the corresponding linear factor to obtain a quadratic polynomial; you can then find the other two roots by factoring the quadratic or using the quadratic formula.

So you only need to find one root using the rational roots theorem. Which ones should you try first?

1 and -1 are always the easiest to test, simply by evaluating the polynomial for those values. In this example, neither 1 nor -1 is a root.

For the other possible rational roots, some students will prefer evaluating the polynomial; other students will find synthetic division easier. Try the smaller integers (positive and negative) first. And hope that you find a root before you need to test the fractions.

In this example, the polynomial evaluated at x=2 is 0, so 2 is a root. Dividing the polynomial by the linear factor (x-2) using synthetic division shows the remaining polynomial to be 2x^2+5x+2. That is easily factored to finish the factorization of the polynomial.
Answer by ikleyn(52799) (Show Source): You can put this solution on YOUR website!
.

The simplest way to solve the problem and to answer the question is TO IGNORE THEIR INSTRUCTION about using the Rational Root theorem, and to factor the given polynomial using the grouping method = + = + = = (x-2)*(x+2)*(2x+1). Thus the correct answers are these and only these A), C), and D).

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I am 129% sure that the original problem (without their instruction on using Rational Root theorem) was designed and intended to be solved exactly in this way, and only later, in its journey over the Internet, this addition was mistakenly made about using the Rational Root theorem.

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