To factor the expression \( 14x + 12x^2 - 2x^3 \), we can follow these steps:

### Step 1: Look for a common factor
Each term has a factor of \( 2x \), so we can factor that out:

\[
14x + 12x^2 - 2x^3 = 2x(7 + 6x - x^2)
\]

### Step 2: Factor the quadratic expression \( 7 + 6x - x^2 \)
Now, we need to factor the quadratic \( 7 + 6x - x^2 \).

Rearranging it to standard form, we get:
\[
-x^2 + 6x + 7 = -(x^2 - 6x - 7)
\]

Now, factor \( x^2 - 6x - 7 \):
\[
x^2 - 6x - 7 = (x - 7)(x + 1)
\]

Thus, we have:
\[
-(x^2 - 6x - 7) = -(x - 7)(x + 1) = -(x + 1)(x - 7)
\]

### Step 3: Put everything together
Now substitute this factorization back into the original expression:
\[
2x(7 + 6x - x^2) = 2x(-(x + 1)(x - 7))
\]

So the fully factored form of the expression is:
\[
\boxed{-2x(x + 1)(x - 7)}
\]

Would you like more details on factoring quadratic expressions or any other step? 

Here are 5 related questions to practice:
1. Factor \( 3x^2 - 12x \).
2. Factor \( 5x + 10x^2 - 15x^3 \).
3. Factor \( 6x^2 + 11x - 10 \).
4. Factor \( -4x^2 + 8x + 16 \).
5. Factor \( x^2 - 9x + 20 \).

**Tip:** Always start by factoring out the greatest common factor (GCF) before factoring further.

Learn how to factor the polynomial expression 14x + 12x^2 − 2x^3 step-by-step. This problem focuses on factoring out the greatest common factor (GCF) and factoring quadratic expressions. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation