Select all polynomials that have a zero located at (4,0) f(x)=(x-5)(x+4) f(x)=(2x-8)(x+5) f(x)=4x(x-3)(x-1) f(x)=(x-4)(x-3)(x+1) f(x)=2x(4-x)(x+5)(3x-4)

To determine which polynomials have a zero located at $(4,0)$, we need to find the values of $x$ for which the polynomial equals zero.<br /><br />Let's analyze each polynomial:<br /><br />1. $f(x)=(x-5)(x+4)$<br /> - This polynomial has zeros at $x=5$ and $x=-4$. It does not have a zero at $x=4$.<br /><br />2. $f(x)=(2x-8)(x+5)$<br /> - This polynomial has zeros at $x=4$ and $x=-5$. It has a zero at $x=4$.<br /><br />3. $f(x)=4x(x-3)(x-1)$<br /> - This polynomial has zeros at $x=0$, $x=3$, and $x=1$. It does not have a zero at $x=4$.<br /><br />4. $f(x)=(x-4)(x-3)(x+1)$<br /> - This polynomial has zeros at $x=4$, $x=3$, and $x=-1$. It has a zero at $x=4$.<br /><br />5. $f(x)=2x(4-x)(x+5)(3x-4)$<br /> - This polynomial has zeros at $x=0$, $x=4$, $x=-5$, and $x=\frac{4}{3}$. It has a zero at $x=4$.<br /><br />Therefore, the polynomials that have a zero located at $(4,0)$ are:<br />- $f(x)=(2x-8)(x+5)$<br />- $f(x)=(x-4)(x-3)(x+1)$<br />- $f(x)=2x(4-x)(x+5)(3x-4)$