Find the Common Factor of 2ax+4x²: Step-by-Step Solution

To solve this problem, we'll employ the method of factoring by common factor:

• Step 1: Identify the common factor in the terms $2ax$ and $4x^2$.
• Step 2: Factor out the common factor.
• Step 3: Verify the factored form by expanding to ensure it equals the original expression.

Let's begin with Step 1:

Looking at the terms $2ax$ and $4x^2$, we can see that both terms include $x$ as a common factor. They also share the coefficient '2'. Therefore, the greatest common factor (GCF) is $2x$.

In Step 2, we'll factor $2x$ out of each of the terms:

$2ax$ becomes $2x \cdot a$, and
$4x^2$ becomes $2x \cdot 2x$.

So the expression can be written as:

$2ax + 4x^2 = 2x(a) + 2x(2x)$

Thus, factored completely using the common factor $2x$:

$2ax + 4x^2 = 2x(a + 2x)$

In Step 3, let’s verify by expanding:

Expanding $2x(a + 2x)$, we have:

$2x \cdot a + 2x \cdot 2x = 2ax + 4x^2$,
which confirms our factorization is correct.

Therefore, the solution to the problem is $2x(a + 2x)$.