Question
Finish factoring by grouping. There is one more step. \[ \begin{array}{l}x^{2}+3 x+2 x+6 \\ \left(x^{2}+3 x\right)+(2 x+6) \\ x(x+3)+2(x+3)\end{array} \]
Ask by Adkins Pearson. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( (x + 3)(x + 2) \)
Solution
After factoring by grouping, you have:
x(x + 3) + 2(x + 3)
Notice that (x + 3) is a common factor in both terms. Factor (x + 3) out:
(x + 3)(x + 2)
This is the fully factored form.
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Simplify this solution Mind Expander
Great start! You’ve grouped and factored the expression nicely. Now, notice that both terms contain the common factor \( (x+3) \). You can factor that out for the next step. So, you can rewrite it as: \[ (x+3)(x+2) \] And voilà! That’s the fully factored form of the original expression! If you plug the factors back into the equation, you're back to where you started, proving that your work is spot on. Keep up the fantastic mathematical feats!
