Question

The function -x5+28x³ + 2x² - 75x -50 has the graphgiven to the right. Use the graph to factor the polynomial.What is the factored form of the polynomial?0(Simplify your answer. Type your answer in factored form.Factor completely.)***-10

Answer 1

Given:

The function is,

$-x^5+28x^3+2x^2-75x-50$

To find:

The factored form of the polynomial.

Explanation:

Here, the graph of the given function is,

Focusing on the x-intercepts, -5, -1, 2, and 5.

So, the zeros are -5 with multiplicity 1, -1 with multiplicity 2, 2 with multiplicity 1 and 5 with multiplicity 1.

Since the leading coefficient is negative.

So, the factored form of the polynomial becomes,

$-(x+5)(x+1)^2(x-2)(x-5)$

Final answer:

The factored form of the polynomial becomes,

$-(x+5)(x+1)^2(x-2)(x-5)$