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# polynomial help

Consider the polynomial P(x), shown in both standard form and factored form. P(x)=−1/3 x^4 −1/3 x^3 +7/3 x^2 +1/3 x−2=−1/3 (x+3)(x+1)(x−1)(x−2)

State the zeros of the function.

State the y-intercept.

### 2 Answers by Expert Tutors

Jane B. | Master's degree in Education. Focus on success for all students.Master's degree in Education. Focus on s...
4.8 4.8 (5 lesson ratings) (5)
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Theresa, you wrote the initial factored problem as P(x) = −1/3 (x+3) (x+1) (x−1) (x−2).

In order to "state the 'zeros' of the function," we have to see what values of x will make P(x) = 0.

Each of the elements are multiplied, so if any one element is equal to 0, then the entire set becomes equal to 0.

Step 1) -1/3 can't be changed, because it's not multiplied by x.
Step 2) (x+3) = 0 if x = -3
Step 3) (x+1) = 0 if x = -1
Step 4) (x-1) = 0 if x = 1
Step 5) (x-2) = 0 if x = 2

Therefore, your solution set is {-3, -1, 1, 2}

No need for one tutor to overpost another, Jane.  I was trying to get the student to do some of the work, rather than handing her the answer.   There are plenty of unanswered questions to answer.
Philip P. | Effective and Affordable Math TutorEffective and Affordable Math Tutor
5.0 5.0 (438 lesson ratings) (438)
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Use the "zero factor property" - find the value of x that sets each factor to zero.

P(x) = −1/3 (x+3)(x+1)(x−1)(x−2)

P(x) will = 0 when (x+3)=0 or (x+1)=0 or (x-1)=0 or (x-2)=0

The first factor is (x+3).  The value of x = -3 will make it equal zero, so x = -3 is one the points.  Can you find the other values for the other factors?

The y-intercept occurs when x = 0.  Set x = 0 in P(x) to find the y-intercept.