giannisdagoat
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Which shows one way to determine the factors of [tex]\( x^3 + 11x^2 - 3x - 33 \)[/tex] by grouping?

A. [tex]\( x^2(x + 11) + 3(x - 11) \)[/tex]

B. [tex]\( x^2(x - 11) - 3(x - 11) \)[/tex]

C. [tex]\( x^2(x + 11) + 3(x + 11) \)[/tex]

D. [tex]\( x^2(x + 11) - 3(x + 11) \)[/tex]

Sagot :

GinnyAnswer
To factor the polynomial [tex]\( x^3 + 11x^2 - 3x - 33 \)[/tex] by grouping, follow these steps:

1. Group the terms in pairs:
[tex]\[ (x^3 + 11x^2) + (-3x - 33) \][/tex]

2. Factor out the greatest common factor (GCF) from each pair of terms:
- For the first pair [tex]\( x^3 + 11x^2 \)[/tex], the GCF is [tex]\( x^2 \)[/tex].
[tex]\[ x^2(x + 11) \][/tex]
- For the second pair [tex]\( -3x - 33 \)[/tex], the GCF is [tex]\( -3 \)[/tex].
[tex]\[ -3(x + 11) \][/tex]

3. Combine the factored forms:
[tex]\[ x^2(x + 11) - 3(x + 11) \][/tex]

Thus, the correct way to determine the factors by grouping is:
[tex]\[ x^2(x + 11) - 3(x + 11) \][/tex]

So, the correct option is:
[tex]\[ x^2(x + 11) - 3(x + 11) \][/tex]
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