3.5. Alice was provided with the following trinomial; 3x² + 7x - 12x - 2x² + 10 3.5.1. provide Alice with a step by step guide on how to factorize the algebraic expression.?

To factorize the given trinomial 3x² + 7x - 12x - 2x² + 10, follow these steps:

Step 1: Combine like terms
Combine the like terms in the expression:
3x² - 2x² + 7x - 12x + 10

Step 2: Simplify the expression
Simplify the expression by combining the like terms:
x² - 5x + 10

Step 3: Factorize the trinomial
To factorize the trinomial x² - 5x + 10, you need to find two numbers that multiply to the constant term (10) and add up to the coefficient of the middle term (-5). In this case, the numbers are -2 and -3:
(x - 2)(x - 3)

Therefore, the factorized form of the given trinomial 3x² + 7x - 12x - 2x² + 10 is (x - 2)(x - 3).

Step-by-Step Guide to Factorizing:

3.5.1. Group Like Terms:

- Group the terms with x² together: 3x² - 2x² = x²
- Group the terms with x together: 7x - 10x = -3x

3.5.2. Factor Out the Greatest Common Factor (GCF):

From the grouped terms, the GCF is x

- x² = x - x
- -3x = x - (-3)

3.5.3. Factor Out the GCF from Each Group:

- Factor out x from x²: x² = x(x)
- Factor out x from -3x: -3x = x(-3)

3.5.4. Put the Factored Terms Together:

- The original expression becomes: x(x - 3) + 10

3.5.5. Check the Factorization:

- Multiply the factors together: x(x - 3) = x² - 3x
- Add 10 to the product: x² - 3x + 10

Result: The factorized expression is: x(x - 3) + 10

35-12

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