Find Expressions Equivalent to 8x²+4x: Polynomial Practice

Let's solve the problem step by step:

• Step 1: Identify the greatest common factor (GCF) of the coefficients in the expression $8x^2 + 4x$. The numbers are 8 and 4, and the GCF is 4.

• Step 2: Factor out the common variable. Both terms have $x$ as a common variable factor, so the GCF of the variable part is $x$.

• Step 3: Factor the expression using the GCF. We take $4x$ as a common factor from both terms:
      $8x^2$ can be rewritten as $4x \cdot 2x$.
      $+4x$ can be rewritten as $4x \cdot 1$.

• Step 4: Write the factored expression:
      $8x^2 + 4x = 4x(2x + 1)$.

• Step 5: Verify by checking each option. The expression we obtained $4x(2x + 1)$ matches the choice with 2.

Therefore, the equivalent expression is $4x(2x+1)$.