The factors of a polynomial are (x + 3)(x - 2)(x + 7). How do the zeros relate to the factors?
Can someone explain this to me because I am so lost?
The zeros are always the opposite sign of their value in the factors.
Example:
(x-2)
The value in this factor is -2 but when you solve for x to find your zero it would be +2.
Certainly! I can help you with understanding the relationship between the factors of a polynomial and its zeros.
To begin, let's understand what zeros of a polynomial are. Zeros, also called roots, are the values of 'x' that make the polynomial equal to zero. In other words, they are the values that solve the polynomial equation when it is set to zero.
Now, in your case, the factors of the polynomial are given as (x + 3)(x - 2)(x + 7). When factoring a polynomial, we break it down into simpler expressions called factors. In this case, we have three factors: (x + 3), (x - 2), and (x + 7).
To find the zeros of the polynomial, we set each factor equal to zero and solve for 'x' separately:
Setting (x + 3) = 0, we get:
x + 3 = 0
x = -3
Setting (x - 2) = 0, we get:
x - 2 = 0
x = 2
Setting (x + 7) = 0, we get:
x + 7 = 0
x = -7
So, the zeros of the polynomial (also known as the solutions to the equation) are x = -3, x = 2, and x = -7.
The relationship between the factors of the polynomial and its zeros is that each factor corresponds to a particular zero. In this case, the factor (x + 3) corresponds to the zero x = -3, the factor (x - 2) corresponds to the zero x = 2, and the factor (x + 7) corresponds to the zero x = -7.
Therefore, if you set the polynomial equal to zero and solve for 'x', you will find that the zeros of the polynomial are exactly the values that make each factor equal to zero.
I hope this explanation clears up your confusion! Let me know if you have any further questions.