The function

*f*is defined as f(x) = x(x² - 4) - 3x(x - 2).
Part AAn equivalent form of f is given as f(x) = x(x - 2)(x - a), where a is a constant. What is the value of a? |
Part BWhich values are zeros of the function, f?Select all that apply. A.) -3 E.) 1 B.) -2 F.) 2 C.) -1 G.) 3 D.) 0 |

__Part A__

**f(x) = x(x² - 4) - 3x(x - 2)**

and

f(x) = x(x - 2)(x - a)

are equivalent. Find the value of a.

and

f(x) = x(x - 2)(x - a)

are equivalent. Find the value of a.

Therefore,

x(x² - 4) - 3x(x - 2) = x(x - 2)(x - a) {set the functions equal to each other}

x(x + 2)(x - 2) - 3x(x - 2) = x(x - 2)(x - a) {factored the x² - 4 into (x + 2)(x - 2)}

x + 2 - 3 = x - a {divided each side by x(x - 2)}

x - 1 = x - a {combined like terms}

-a = -1 {subtracted x from each side}

**a = 1**{divided each side by -1}

**Part B****Which values are zeros of the function, f?**

f(x) = x(x - 2)(x - 1) {replaced a with 1 in the equivalent form, because it is already factored}

x(x - 2)(x - 1) = 0 {substituted 0, for f(x), to find the zeros}

x = 0 or x - 2 = 0 or x - 1 = 0 {set each factor equal to 0}

x = 0 or x = 2 or x = 1 {solved each equation for x}

**D.) 0, E.) 1, and F.) 2 are the zeros**

**Ask Algebra House**