To factor quadratic equations when the first number is greater than one, follow these simple steps:

1. Identify the equation: Look for an equation that looks like this: $ax^2 + bx + c$, where $a$ is more than 1.

2. Multiply: Multiply $a$ and $c$ together to get a new number called $ac$.

3. Find factors: Search for two numbers that multiply together to give you $ac$ and also add up to $b$.

4. Split the middle term: Use the two numbers you found to rewrite $bx$.

5. Group and factor: Group the terms together and factor them.

Let's go through an example using $2x^2 + 7x + 3$:

• First, we calculate $ac$:

  • $2 \times 3 = 6$.

• Next, we need to find two numbers:

  • The numbers are $6$ and $1$ because $6 + 1 = 7$.

• Now we can rewrite the equation:

  • Change $7x$ to $6x + 1x$:
  • So, we write it like this: $2x^2 + 6x + 1x + 3$.

• Next, we group the terms:

  • We can group it as: $(2x^2 + 6x) + (1x + 3)$.

• Then we factor each group:

  • For the first group, we factor out $2x$:
  • This gives us $2x(x + 3)$.
  • For the second group, we factor out $1$:
  • So we have $1(x + 3)$.

• Finally, we combine everything together:

  • We get the factored form: $(2x + 1)(x + 3)$.

And that’s how you factor a quadratic equation when the first number is more than one!