**P(x) = −1/3 (x+3) (x+1) (x−1) (x−2).**

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.

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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}

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.

is the y intercept (0,-2)

and i am not understanding the zero factor property

Yes, the y-intercept is (0,-2). You'll note that it's the constant term in the polynomial; that is, the one term not multiplied by x.

If you look at the factored form, it's four factors multiplied together. Any number multiplied by zero is zero. So if any one of the factors equals zero, the whole polynomial equals 0 (P = 0). So if (x+1)=0, then P=0. (x+1)=0 when x=-1. So (-1,0) is one of the P=0 points. There are 3 others, one for each of the remaining three factors.

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