$$ 1 \leftarrow \quad $$ Factor by grouping. $$ x^{3}-2 x^{2}+3 x-6 $$ Select the correct choice below and fill in any answer boxes within your choice. A. $$ x^{3}-2 x^{2}+3 x-6=\square $$ B. The polynomial is prime.

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UpStudy AI · Accepted Answer

1. Write the polynomial as two groups:
   $$
   x^3 - 2x^2 + 3x - 6 = (x^3 - 2x^2) + (3x - 6)
   $$

2. Factor out the common factor from each group:
   $$
   x^3 - 2x^2 = x^2(x - 2) \quad \text{and} \quad 3x - 6 = 3(x - 2)
   $$

3. Rewrite the expression with the common factor $$(x - 2)$$:
   $$
   x^3 - 2x^2 + 3x - 6 = x^2(x - 2) + 3(x - 2) = (x - 2)(x^2 + 3)
   $$

Thus, the factorization is:

A. $$ x^{3}-2 x^{2}+3 x-6=(x-2)(x^2+3) $$
$$ x^{3}-2 x^{2}+3 x-6=(x-2)(x^2+3) $$

\( 1 \leftarrow \quad \) Factor by grouping. \[ x^{3}-2 x^{2}+3 x-6 \] Select the correct choice below and fill in any answer boxes within your choice. A. \( x^{3}-2 x^{2}+3 x-6=\square \) B. The polynomial is prime.

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