Question

find a polynomial function that has the given zeros. (there are many correct ans -5, 4 f(x) = resources read it watch it

Explanation:

Step1: Recall the factor theorem

If \( r \) is a zero of a polynomial, then \( (x - r) \) is a factor of the polynomial. Given zeros \( -5 \) and \( 4 \), the corresponding factors are \( (x - (-5))=(x + 5) \) and \( (x - 4) \).

Step2: Multiply the factors

To find the polynomial, we multiply these factors together. So \( f(x)=(x + 5)(x - 4) \).
Expanding this using the distributive property (FOIL method):
\( (x + 5)(x - 4)=x\times x+x\times(-4)+5\times x + 5\times(-4)=x^{2}-4x + 5x-20=x^{2}+x - 20 \). (We can also have other polynomials by multiplying this by a non - zero constant, but a simple one is obtained by taking the product of the linear factors with leading coefficient 1)

Answer:

\( x^{2}+x - 20 \) (or any non - zero multiple of it, e.g., \( 2x^{2}+2x - 40 \) etc. But the simplest one is \( x^{2}+x - 20 \))