🔢 Key Terms: Zeros of Polynomials

1. Zero of a Polynomial
   A number that, when substituted for x, makes the entire polynomial equal to zero.
   👉 Example: If f(x)=x2−4f(x) = x^2 - 4f(x)=x2−4, then x=2x = 2x=2 and x=−2x = -2x=−2 are zeros because f(2)=0f(2) = 0f(2)=0 and f(−2)=0f(-2) = 0f(−2)=0.
   
   

2. Root
   Another word for a zero of a polynomial. They mean the same thing!
   👉 Think of it as: roots = zeros = solutions.
   
   

3. Solution
   A value of x that makes the equation f(x)=0f(x) = 0f(x)=0 true.
   👉 When you solve a polynomial equation, you're finding its solutions (which are the same as zeros and roots).
   
   

4. x-intercept
   The point(s) where the graph of the polynomial crosses or touches the x-axis.
   👉 These points have the form (x,0)(x, 0)(x,0), and the x-values are the zeros.
   👉 Example: If the graph crosses the x-axis at (3,0)(3, 0)(3,0), then 3 is a zero of the polynomial.