Answer :

Answer:

[tex](x+7)(3x+ 1)[/tex]

Step-by-step explanation:

We can factor the trinomial:

[tex]3x^2 + 22x+ 7[/tex]

by grouping.

First, we multiply the constant by the x² term's coefficient:

[tex]3 \cdot 7 =21[/tex]

Then, we list out the factor pairs and select the one whose factors add to the middle term's coefficient (21):

  • (1, 21)
  • (3, 7)

Next, we can split the middle term using the factors we selected as coefficients:

[tex]3x^2 + 1x + 21x+ 7[/tex]

Now, we can factor out the GCF of the first two and last two terms:

[tex]x(3x + 1) + 7(3x+ 1)[/tex]

Finally, we can rewrite the expression using the distributive property:

[tex]\boxed{(x+7)(3x+ 1)}[/tex]