Factor the following expression completely. x^(4)-6x^(3)-7x^(2)-9x^(2)+54 x+63 Answer:

Combine Like Terms: First, let's combine like terms in the expression. x^4 - 6x^3 - 7x^2 - 9x^2 + 54x + 63 = x^4 - 6x^3 - (7 + 9)x^2 + 54x + 63 = x^4 - 6x^3 - 16x^2 + 54x + 63Factor by Grouping: Next, we look for common factors or patterns that might help us factor the expression. We can try to factor by grouping, which involves grouping terms to find a common factor. Group the terms as follows: (x^4 - 6x^3) - (16x^2 - 54x) + 63 Now, factor out the common factors from each group. x^3(x - 6) - 2x(8x - 27) + 63Identify Math Error: We notice that the last term, 63, does not fit into the pattern of the grouped terms. We need to see if there is a common factor that can be factored out from all terms or if there is a mistake in the previous step. Upon reviewing the previous step, we realize that we cannot factor out -2x from (16x^2 - 54x) because -2 is not a factor of 54. This is a math error.

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Q. Factor the following expression completely.

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x^{4}-6 x^{3}-7 x^{2}-9 x^{2}+54 x+63

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Answer:

Combine Like Terms: First, let's combine like terms in the expression. $\newline$ $x^4 - 6x^3 - 7x^2 - 9x^2 + 54x + 63$ $\newline$ = $x^4 - 6x^3 - (7 + 9)x^2 + 54x + 63$ $\newline$ = $x^4 - 6x^3 - 16x^2 + 54x + 63$
Factor by Grouping: Next, we look for common factors or patterns that might help us factor the expression. We can try to factor by grouping, which involves grouping terms to find a common factor. $\newline$ Group the terms as follows: $\newline$ $(x^4 - 6x^3) - (16x^2 - 54x) + 63$ $\newline$ Now, factor out the common factors from each group. $\newline$ $x^3(x - 6) - 2x(8x - 27) + 63$
Identify Math Error: We notice that the last term, $63$ , does not fit into the pattern of the grouped terms. We need to see if there is a common factor that can be factored out from all terms or if there is a mistake in the previous step. $\newline$ Upon reviewing the previous step, we realize that we cannot factor out $-2x$ from $(16x^2 - 54x)$ because $-2$ is not a factor of $54$ . This is a math error.