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Factor completely: x^(2)(x+3)-7x(x+3)+6(x+3) Answer:

Factor completely:\newlinex2(x+3)−7x(x+3)+6(x+3) x^{2}(x+3)-7 x(x+3)+6(x+3) \newlineAnswer:

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Full solution

Q. Factor completely:\newlinex2(x+3)−7x(x+3)+6(x+3) x^{2}(x+3)-7 x(x+3)+6(x+3) \newlineAnswer:
  1. Identify Common Factor: Identify the common factor in all terms.\newlineThe expression is x2(x+3)−7x(x+3)+6(x+3)x^{2}(x+3)-7x(x+3)+6(x+3). Each term contains the factor (x+3)(x+3).
  2. Factor Out Common Factor: Factor out the common factor (x+3)(x+3). We can write the expression as (x+3)(x2−7x+6)(x+3)(x^2 - 7x + 6).
  3. Factor Quadratic Expression: Factor the quadratic expression.\newlineThe quadratic expression x2−7x+6x^2 - 7x + 6 can be factored into (x−1)(x−6)(x - 1)(x - 6) because (x−1)(x−6)=x2−6x−x+6=x2−7x+6(x - 1)(x - 6) = x^2 - 6x - x + 6 = x^2 - 7x + 6.
  4. Write Completely Factored Form: Write the completely factored form.\newlineThe completely factored form of the original expression is (x+3)(x−1)(x−6)(x+3)(x-1)(x-6).

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