Create a polynomial \( p \) that has the desired characteristics. You may leave the polynomial in factored form. - The \( x \) intercepts of \( p \) are \( (6,0),(9,0),(-4,0) \) and \( (-5,0) \). - The leading term of \( p \) is \( 125 x^{4} \). \( p(x)= \)

To create the polynomial \( p \) with the given \( x \) intercepts and leading term, we can start by writing the polynomial in factored form based on the intercepts. The factors corresponding to the \( x \) intercepts \( (6,0), (9,0), (-4,0), \) and \( (-5,0) \) are: \[ p(x) = k(x - 6)(x - 9)(x + 4)(x + 5) \] Here, \( k \) is a constant that we will determine in order to set the leading term to \( 125 x^4 \). Since the polynomial is degree 4 (four factors), we can expand the product: 1. The leading coefficient from each factor is multiplied: - The leading coefficient of each binomial in our factors is \( 1 \). Hence the leading term from the product of these 4 factors is \( x^4 \). So we want to find \( k \) such that: \[ k \cdot 1 = 125 \] This gives us: \[ k = 125 \] Thus, the polynomial in factored form is: \[ p(x) = 125(x - 6)(x - 9)(x + 4)(x + 5) \] This polynomial has the desired \( x \) intercepts and the correct leading term.