I need help with all of them plz. ## Solving Polynomial Equations by Factoring### Example Problem: **Solve:** $ 6x^3 + 12x = 17x^2 $This equation is not quadratic because it contains a term involving $ x^3 $. However, we can solve it by using factoring. First, we get 0 on the right side by subtracting $ 17x^2 $ from both sides. Then, we factor the polynomial on the left side and use an extension of the zero-factor property.**Step-by-Step Solution:**1. **Rewrite the equation to set one side to 0:** \[ 6x^3 + 12x - 17x^2 = 0 \] This is achieved by subtracting $ 17x^2 $ from both sides: \[ 6x^3 + 12x - 17x^2 = 17x^2 - 17x^2 \implies 6x^3 - 17x^2 + 12x = 0 \]2. **Factor out the greatest common factor (GCF):** \[ x(6x^2 - 17x + 12) = 0 \]3. **Factor the trinomial:** \[ x(2x - 3)(3x - 4) = 0 \]4. **Apply the zero-factor property:** If $ x(2x - 3)(3x - 4) = 0 $, then at least one of the factors must be zero. \[ x = 0 \quad \text{or} \quad 2x - 3 = 0 \quad \text{or} \quad 3x - 4 = 0 \]5. **Solve each equation:** - $ x = 0 $ - $ 2x - 3 = 0 \implies 2x = 3 \implies x = \frac{3}{2} $ - $ 3x - 4 = 0 \implies 3x = 4 \implies x = \frac{4}{3} $**Solution Set:**The solutions are $ 0 $, \( 3/

The zeroes of a function in a variable are the values of the variable at which the value of the…

This equation is not quadratic, because it contains a term involving x³. However, we can solve it by using factoring. First we get 0 on the right side by subtracting 17x2 from both sides. Then we factor the polynomial on the left side and use an extension of the zero-factor property.

This equation is not quadratic, because it contains a term involving x³. However, we can solve it by using factoring. First we get 0 on the right side by subtracting 17x2 from both sides. Then we factor the polynomial on the left side and use an extension of the zero-factor property.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

I need help with all of them plz.

## Solving Polynomial Equations by Factoring

### Example Problem:

**Solve:** $ 6x^3 + 12x = 17x^2 $

This equation is not quadratic because it contains a term involving $ x^3 $. However, we can solve it by using factoring. First, we get 0 on the right side by subtracting $ 17x^2 $ from both sides. Then, we factor the polynomial on the left side and use an extension of the zero-factor property.

**Step-by-Step Solution:**

1. **Rewrite the equation to set one side to 0:**
\[
6x^3 + 12x - 17x^2 = 0
\]

This is achieved by subtracting $ 17x^2 $ from both sides:
\[
6x^3 + 12x - 17x^2 = 17x^2 - 17x^2 \implies 6x^3 - 17x^2 + 12x = 0
\]

2. **Factor out the greatest common factor (GCF):**
\[
x(6x^2 - 17x + 12) = 0
\]

3. **Factor the trinomial:**
\[
x(2x - 3)(3x - 4) = 0
\]

4. **Apply the zero-factor property:**
If $ x(2x - 3)(3x - 4) = 0 $, then at least one of the factors must be zero.

\[
x = 0 \quad \text{or} \quad 2x - 3 = 0 \quad \text{or} \quad 3x - 4 = 0
\]

5. **Solve each equation:**
- $ x = 0 $
- $ 2x - 3 = 0 \implies 2x = 3 \implies x = \frac{3}{2} $
- $ 3x - 4 = 0 \implies 3x = 4 \implies x = \frac{4}{3} $

**Solution Set:**

The solutions are $ 0 $, \( 3/

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