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Factor by grouping:

\[ x^3 + 5x^2 + 9x + 45 \]

\[ x^3 + 5x^2 + 9x + 45 = \]

Answer :

To factor the expression [tex]\(x^3 + 5x^2 + 9x + 45\)[/tex] by grouping, follow these steps:

1. Group the Terms:
Divide the expression into two groups:
[tex]\[
(x^3 + 5x^2) + (9x + 45)
\][/tex]

2. Factor Each Group:
- First Group: [tex]\(x^3 + 5x^2\)[/tex]
- Factor out the greatest common factor, [tex]\(x^2\)[/tex]:
[tex]\[
x^2(x + 5)
\][/tex]

- Second Group: [tex]\(9x + 45\)[/tex]
- Factor out the greatest common factor, 9:
[tex]\[
9(x + 5)
\][/tex]

3. Combine the Factored Terms:
Now, the expression looks like this:
[tex]\[
x^2(x + 5) + 9(x + 5)
\][/tex]

4. Factor Out the Common Binomial Factor:
The common factor in each term is [tex]\((x + 5)\)[/tex]. Factor this out:
[tex]\[
(x + 5)(x^2 + 9)
\][/tex]

This gives the fully factored form of the expression:
[tex]\[
(x + 5)(x^2 + 9)
\][/tex]

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Rewritten by : Barada