QuestionJuly 28, 2025

Factor completely. 3x^2-3x-90 square

Factor completely. 3x^2-3x-90 square
Factor completely.
3x^2-3x-90
square

Solution
4.6(144 votes)

Answer

3(x - 6)(x + 5) Explanation 1. Factor out the greatest common factor The greatest common factor of 3x^2 - 3x - 90 is 3. Factor it out: 3(x^2 - x - 30). 2. Factor the quadratic expression Find two numbers that multiply to -30 and add to -1. These numbers are -6 and 5. Rewrite the middle term: x^2 - 6x + 5x - 30. 3. Group terms and factor by grouping Group: (x^2 - 6x) + (5x - 30). Factor each group: x(x - 6) + 5(x - 6). 4. Factor out the common binomial Factor out (x - 6): (x - 6)(x + 5).

Explanation

1. Factor out the greatest common factor<br /> The greatest common factor of $3x^2 - 3x - 90$ is 3. Factor it out: $3(x^2 - x - 30)$.<br />2. Factor the quadratic expression<br /> Find two numbers that multiply to -30 and add to -1. These numbers are -6 and 5. Rewrite the middle term: $x^2 - 6x + 5x - 30$.<br />3. Group terms and factor by grouping<br /> Group: $(x^2 - 6x) + (5x - 30)$. Factor each group: $x(x - 6) + 5(x - 6)$.<br />4. Factor out the common binomial<br /> Factor out $(x - 6)$: $(x - 6)(x + 5)$.
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