Question

question 7 (multiple choice worth 5 points) (03.03r mc) one zero of the polynomial function f(x) = x³ + x² - 20x is x = 0. what are the zeros of the polynomial function? 0, -5, -4 0, -5, 4 0, 5, -4 0, 5, 4

Explanation:

Step1: Factor the polynomial

Given \( f(x) = x^3 + x^2 - 20x \), we can factor out an \( x \) first: \( f(x)=x(x^2 + x - 20) \).

Step2: Factor the quadratic

Now, factor the quadratic \( x^2 + x - 20 \). We need two numbers that multiply to \(-20\) and add to \(1\). Those numbers are \(5\) and \(-4\), so \( x^2 + x - 20=(x + 5)(x - 4) \).

Step3: Find the zeros

Putting it all together, \( f(x)=x(x + 5)(x - 4) \). To find the zeros, set \( f(x)=0 \), so \( x = 0 \), \( x + 5 = 0\) (which gives \( x=-5 \)), or \( x - 4 = 0\) (which gives \( x = 4 \)). So the zeros are \( 0, -5, 4 \).

Answer:

0, -5, 4 (corresponding to the option with these values, likely the third option in the list)