We want to factor the following expression: x^(4)+9 Which pattern can we use to factor the expression? U and V are either constant integers or single-variable expressions. Choose 1 answer: (A) (U+V)^(2) or (U-V)^(2) (B) (U+V)(U-V) (c) We can't use any of the patterns.

Question

We want to factor the following expression:  x^(4)+9 Which pattern can we use to factor the expression?  U and  V are either constant integers or single-variable expressions. Choose 1 answer: (A)  (U+V)^(2) or  (U-V)^(2) (B)  (U+V)(U-V) (c) We can't use any of the patterns.

Bytelearn · Accepted Answer

Step 1: Determine Factoring Pattern: The expression x^(4)+9 is a sum of two terms, where one term is x raised to the fourth power and the other term is a constant 9. We need to determine if there is a factoring pattern that applies to this expression.Step 2: Evaluate Option (A): Option (A) suggests using the square of a binomial pattern, either (U+V)^(2) or (U-V)^(2). However, these patterns expand to U^2 + 2UV + V^2 and U^2 - 2UV + V^2, respectively. Neither of these patterns match the given expression x^(4)+9 because there is no middle term in the expression x^(4)+9.Step 3: Evaluate Option (B): Option (B) suggests using the difference of squares pattern, (U+V)(U-V), which expands to U^2 - V^2. This pattern also does not apply because we have a sum, not a difference, and the expression x^(4)+9 does not represent a difference of squares.Step 4: Evaluate Option (C): Option (C) states that we can't use any of the patterns. Since neither the square of a binomial pattern nor the difference of squares pattern applies to the expression x^(4)+9, and there are no other common factoring patterns for a sum of a fourth power and a constant, we conclude that the expression x^(4)+9 cannot be factored using standard algebraic patterns over the real numbers.

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