Answered

Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Select the correct answer from each drop-down menu.

Use the remainder theorem to complete the informal proof for the following statement.

[tex]$x = -5$[/tex] is a root of the function [tex]$f(x) = x^3 + 3x^2 - 25x - 75$[/tex].

1. If [tex]$x = -5$[/tex] is a root of [tex]$f(x)$[/tex], then [tex]$(x + 5)$[/tex] must be _____.
2. Find the [tex]$\square$[/tex] of [tex]$f(x)$[/tex] and [tex]$(x + 5)$[/tex].
3. The [tex]$\square$[/tex] of this operation is 0.
4. Thus, [tex]$(x + 5)$[/tex] is _____ [tex]$f(x)$[/tex].
5. Therefore, [tex]$x = -5$[/tex] is a root of [tex]$f(x)$[/tex].

Sagot :

GinnyAnswer
Sure, let's use the remainder theorem and the given answer to complete this proof step-by-step.

1. If [tex]\(x = -5\)[/tex] is a root of [tex]\(f(x)\)[/tex], then [tex]\((x + 5)\)[/tex] must be a factor of [tex]\(f(x)\)[/tex].

2. Find the remainder of [tex]\(f(x)\)[/tex] when divided by [tex]\((x + 5)\)[/tex].

3. The result of this operation is 0.

4. Thus, [tex]\((x + 5)\)[/tex] is a factor of [tex]\(f(x)\)[/tex].

5. Therefore, [tex]\(x = -5\)[/tex] is a root of [tex]\(f(x)\)[/tex].
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.