(x^2+x-6)(2x^2+4x) Factored

2 min read Jun 17, 2024
(x^2+x-6)(2x^2+4x) Factored

Factoring (x² + x - 6)(2x² + 4x)

This problem involves factoring a product of two polynomials. Here's how to approach it:

Step 1: Factor each individual polynomial

  • x² + x - 6: This is a quadratic trinomial. We need to find two numbers that add up to 1 (the coefficient of the x term) and multiply to -6 (the constant term). These numbers are 3 and -2. Therefore: x² + x - 6 = (x + 3)(x - 2)

  • 2x² + 4x: This expression has a common factor of 2x. Factoring it out, we get: 2x² + 4x = 2x(x + 2)

Step 2: Combine the factored expressions

Now that we've factored each polynomial, we can substitute them back into the original expression:

(x² + x - 6)(2x² + 4x) = (x + 3)(x - 2) * 2x(x + 2)

Step 3: Simplify (optional)

While this is the completely factored form, we can simplify it further by rearranging the terms:

(x + 3)(x - 2) * 2x(x + 2) = 2x(x + 3)(x - 2)(x + 2)

Final Answer

The fully factored form of (x² + x - 6)(2x² + 4x) is 2x(x + 3)(x - 2)(x + 2).

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