Question

#2. Which expression is equivalent to the trinomial?
Type your answers to each problem in the table below. The order of the factors doesn't matter, but use parentheses around each one! 3x^2 + 22x + 7

Answer 1

To factor the trinomial \(3x^2 + 22x + 7\), we will look for two numbers that multiply to \(3 \times 7 = 21\) and add to \(22\).

The numbers that work are \(21\) and \(1\).

Now we can rewrite the middle term using these two numbers:
\[
3x^2 + 21x + 1x + 7
\]

Next, we can group the terms:
\[
(3x^2 + 21x) + (1x + 7)
\]

Now, we factor out the common factors in each group:
\[
3x(x + 7) + 1(x + 7)
\]

Next, we can factor out the common binomial \((x + 7)\):
\[
(3x + 1)(x + 7)
\]

Thus, the expression equivalent to the trinomial \(3x^2 + 22x + 7\) is:

\[
(3x + 1)(x + 7)
\]

In the requested format with parentheses around each factor, your answer is:
\[
(3x + 1)(x + 7)
\]