Question

Correctnomial function with the stated properties. Reduce all fractions to lowest terms.Third-degree, with zeros of - 3, - 1, and 2, and passes through the point (3, 5).

Answer 1

Explanation

We must construct a polynomial with the following characteristics:

0. degree: 3,

,

1. zeros: x₁ = -3, x₂ = -1 and x₃ = 2,

,

2. passes through the point (3, 5).

The general form for this polynomial is:

$p(x)=a*(x-x_1)(x-x_2)(x_{}_{}-x_3).$

Where a is a constant factor and x₁, x₂ and x₃ are the zeros of the polynomial.

Replacing the values of the zeros, we have:

$p(x)=a*(x+3)(x+1)(x-2).$

Using the condition that the polynomial passes through (3, 5), we have:

$y=a*(3+3)(3+1)(3-2)=a*24=5.$

Solving for a, we get a = 5/24. Replacing this value in the equation above, we get:

$p(x)=\frac{5}{24}(x+3)(x+1)(x-2).$Answer$p(x)=\frac{5}{24}(x+3)(x+1)(x-2)$