Question

quiz 2.1: graphs of polynomial functions
score: 0/10 answered: 0/5
question 1
find a degree 3 polynomial having zeros 4, -5 and -7 and leading coefficient equal to 1. you can give your answer in factored form.
the polynomial is

Explanation:

Step1: Recall the factor theorem

If a polynomial has a zero \( r \), then \( (x - r) \) is a factor of the polynomial.
Given zeros are \( 4 \), \( -5 \), and \( -7 \). So the factors are \( (x - 4) \), \( (x - (-5))=(x + 5) \), and \( (x - (-7))=(x + 7) \).

Step2: Form the polynomial

Since the leading coefficient is \( 1 \), the polynomial in factored form is the product of these factors. So the polynomial \( P(x)=(x - 4)(x + 5)(x + 7) \).

Answer:

\((x - 4)(x + 5)(x + 7)\)