Factor the expression: 2x^2 + 8x.

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Question: Factor the expression: 2x^2 + 8x.

Options:

Correct Answer: 2x(x + 4)

Solution:

First, we can factor out the greatest common factor, which is 2x. This gives us 2x(x + 4).

Factor the expression: 2x^2 + 8x.

Factor the expression: 2x^2 + 8x.

Step 1: Look at the expression 2x^2 + 8x.
Step 2: Identify the greatest common factor (GCF) of the terms. The GCF of 2x^2 and 8x is 2x.
Step 3: Factor out the GCF (2x) from the expression. This means you divide each term by 2x.
Step 4: Write the expression as 2x multiplied by what is left after factoring out the GCF.
Step 5: The remaining part after factoring out 2x is (x + 4).
Step 6: Combine the GCF and the remaining part to get the factored expression: 2x(x + 4).

Factoring – The process of breaking down an expression into simpler components that, when multiplied together, give the original expression.
Greatest Common Factor (GCF) – The largest factor that divides two or more numbers or terms.