Find Equivalent Expressions for 2xy+x²+3x: Polynomial Simplification

To solve this problem, we'll follow these steps:

• Step 1: Identify the greatest common factor (GCF) in the expression.

• Step 2: Factor out the GCF from the expression.

• Step 3: Compare the factored expression with the choices provided.

Now, let's work through each step:
Step 1: The expression given is $2xy + x^2 + 3x$. The GCF of these terms is $x$ because it appears in each term.
Step 2: Factor out $x$ from each term, which gives:$x(2y + x + 3)$ This rewrites the expression in its factored form.
Step 3: Compare the factored form $x(2y + x + 3)$ with the answer choices.

Choice 1: $2x + 2y + 3$ does not match the factored form.
Choice 2: $x(2y + x + 3)$ exactly matches the factored form.
Choice 3: $2x(y + 4)$ does not match the factored form.
Choice 4: $2x(y + x + 3)$ does not match the factored form.

Therefore, the expression $2xy + x^2 + 3x$ is equivalent to $x(2y + x + 3)$.