Factor the trinomial:

3, x, squared, plus, 7, x, plus, 4
3x
2
+7x+4

1 answer

To factor the trinomial \( 3x^2 + 7x + 4 \), we can look for two numbers that multiply to \( 3 \cdot 4 = 12 \) (the product of the leading coefficient and the constant term) and add up to \( 7 \) (the middle coefficient).

The numbers that meet this criteria are \( 3 \) and \( 4 \) because:

  • \( 3 \times 4 = 12 \)
  • \( 3 + 4 = 7 \)

Next, we can rewrite the middle term \( 7x \) using these two numbers:

\[ 3x^2 + 3x + 4x + 4 \]

Now, we can group the terms:

\[ (3x^2 + 3x) + (4x + 4) \]

Now factor out the greatest common factors from each group:

\[ 3x(x + 1) + 4(x + 1) \]

Now we can factor out the common binomial factor \( (x + 1) \):

\[ (3x + 4)(x + 1) \]

Thus, the factored form of the trinomial \( 3x^2 + 7x + 4 \) is:

\[ (3x + 4)(x + 1) \]