High School

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Factor by grouping:

\[ 9x^4 - 21x^3 + 21x - 49 \]

Answer :

To factor the polynomial [tex]\(9x^4 - 21x^3 + 21x - 49\)[/tex] by grouping, follow these steps:

1. Group the terms:
Start by grouping the polynomial into two pairs:
[tex]\[
(9x^4 - 21x^3) + (21x - 49)
\][/tex]

2. Factor out the greatest common factor (GCF) from each group:

- From the first group [tex]\((9x^4 - 21x^3)\)[/tex], the GCF is [tex]\(3x^3\)[/tex]:
[tex]\[
9x^4 - 21x^3 = 3x^3(3x - 7)
\][/tex]

- From the second group [tex]\((21x - 49)\)[/tex], the GCF is [tex]\(7\)[/tex]:
[tex]\[
21x - 49 = 7(3x - 7)
\][/tex]

3. Factor out the common binomial:
Notice that [tex]\((3x - 7)\)[/tex] is a common factor in both terms:
[tex]\[
3x^3(3x - 7) + 7(3x - 7) = (3x^3 + 7)(3x - 7)
\][/tex]

Thus, the factored form of the polynomial [tex]\(9x^4 - 21x^3 + 21x - 49\)[/tex] is:
[tex]\[
(3x - 7)(3x^3 + 7)
\][/tex]

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Rewritten by : Barada