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Factor completely: 6x(3x-10)+5(3x-10) Answer:

Factor completely:\newline6x(3x−10)+5(3x−10) 6 x(3 x-10)+5(3 x-10) \newlineAnswer:

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Full solution

Q. Factor completely:\newline6x(3x−10)+5(3x−10) 6 x(3 x-10)+5(3 x-10) \newlineAnswer:
  1. Identify common factor: Identify the common factor in both terms.\newlineBoth terms 6x(3x−10)6x(3x-10) and 5(3x−10)5(3x-10) have a common factor of (3x−10)(3x-10).
  2. Factor out common factor: Factor out the common factor (3x−10)(3x-10). The expression can be written as (3x−10)(6x+5)(3x-10)(6x+5) by factoring out the common factor.
  3. Check factored expression: Check the factored expression by distributing to ensure it matches the original expression.\newline(3x−10)(6x+5)=6x(3x)+6x(−10)+5(3x)+5(−10)=18x2−60x+15x−50=18x2−45x−50(3x-10)(6x+5) = 6x(3x) + 6x(-10) + 5(3x) + 5(-10) = 18x^2 - 60x + 15x - 50 = 18x^2 - 45x - 50\newlineSince the original expression is 6x(3x−10)+5(3x−10)6x(3x-10)+5(3x-10), and we have an extra term 18x218x^2 which is not in the original expression, we realize there is a mistake.

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