polynomial help

Question

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.

Answer 1

 

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}

 

 

 

Answer 2

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.