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Answer :
Sure! Let's factor the polynomial by grouping.
The given polynomial is:
[tex]\[ x^3 - 6x^2 + 8x - 48 \][/tex]
Step 1: Group terms in pairs.
We can group the terms as follows:
[tex]\[ (x^3 - 6x^2) + (8x - 48) \][/tex]
Step 2: Factor out the greatest common factor (GCF) from each group.
- In the first group, [tex]\(x^3 - 6x^2\)[/tex], we can factor out [tex]\(x^2\)[/tex]:
[tex]\[ x^2(x - 6) \][/tex]
- In the second group, [tex]\(8x - 48\)[/tex], we can factor out 8:
[tex]\[ 8(x - 6) \][/tex]
Step 3: Notice the common factor.
Both groups now contain the factor [tex]\((x - 6)\)[/tex]:
[tex]\[ x^2(x - 6) + 8(x - 6) \][/tex]
Step 4: Factor out the common factor [tex]\((x - 6)\)[/tex]:
Since [tex]\((x - 6)\)[/tex] is common in both terms, we can factor it out:
[tex]\[ (x^2 + 8)(x - 6) \][/tex]
So, the factored form of the polynomial is:
[tex]\[ x^3 - 6x^2 + 8x - 48 = (x^2 + 8)(x - 6) \][/tex]
Thus, the correct answer is:
A. [tex]\(x^3 - 6x^2 + 8x - 48 = (x^2 + 8)(x - 6)\)[/tex]
The given polynomial is:
[tex]\[ x^3 - 6x^2 + 8x - 48 \][/tex]
Step 1: Group terms in pairs.
We can group the terms as follows:
[tex]\[ (x^3 - 6x^2) + (8x - 48) \][/tex]
Step 2: Factor out the greatest common factor (GCF) from each group.
- In the first group, [tex]\(x^3 - 6x^2\)[/tex], we can factor out [tex]\(x^2\)[/tex]:
[tex]\[ x^2(x - 6) \][/tex]
- In the second group, [tex]\(8x - 48\)[/tex], we can factor out 8:
[tex]\[ 8(x - 6) \][/tex]
Step 3: Notice the common factor.
Both groups now contain the factor [tex]\((x - 6)\)[/tex]:
[tex]\[ x^2(x - 6) + 8(x - 6) \][/tex]
Step 4: Factor out the common factor [tex]\((x - 6)\)[/tex]:
Since [tex]\((x - 6)\)[/tex] is common in both terms, we can factor it out:
[tex]\[ (x^2 + 8)(x - 6) \][/tex]
So, the factored form of the polynomial is:
[tex]\[ x^3 - 6x^2 + 8x - 48 = (x^2 + 8)(x - 6) \][/tex]
Thus, the correct answer is:
A. [tex]\(x^3 - 6x^2 + 8x - 48 = (x^2 + 8)(x - 6)\)[/tex]
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