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):
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]