Identify the common binomial factor.

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To factorize the expression x²(2a+3b) + 3x(2a+3b) + 2(2a+3b), we can identify the common factor. Step 1: Identify the common binomial factor. The term (2a+3b) is common to all three parts of the expression. Step 2: Factor out the common term. Factor out (2a+3b) from the entire expression: (2a+3b)(x² + 3x + 2) Step 3: Factorize the quadratic expression inside the parentheses. We need to factorize x² + 3x + 2. We look for two numbers that multiply to 2 and add up to 3. These numbers are 1 and 2. So, x² + 3x + 2 can be factored as (x+1)(x+2). Step 4: Combine all factors. Substitute the factored quadratic back into the expression: (2a+3b)(x+1)(x+2) The factored expression is: (2a+3b)(x+1)(x+2)

Identify the common binomial factor.

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Step-by-step solution

Identify the common binomial factor.

Factor out the common term.

Factorize the quadratic expression inside the parentheses.

Combine all factors.

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