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Factor completely: (x-7)^(5)+8(x-7)^(4) Answer:

Factor completely:\newline(x−7)5+8(x−7)4 (x-7)^{5}+8(x-7)^{4} \newlineAnswer:

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Full solution

Q. Factor completely:\newline(x−7)5+8(x−7)4 (x-7)^{5}+8(x-7)^{4} \newlineAnswer:
  1. Identify Common Factor: Identify the common factor in both terms.\newlineBoth terms have a common factor of (x−7)4(x-7)^{4}.
  2. Factor Out Common Factor: Factor out the common factor from both terms.\newlineFactor (x−7)4(x-7)^{4} out of the expression to get (x−7)4×[(x−7)+8](x-7)^{4} \times [(x-7) + 8].
  3. Simplify Expression: Simplify the expression inside the brackets. Combine like terms inside the brackets to get (x−7)+8(x-7) + 8, which simplifies to x+1x + 1.
  4. Write Final Factored Form: Write the final factored form.\newlineThe factored form of the expression is (x−7)4×(x+1)(x-7)^{4} \times (x + 1).

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