Factor completely. 3x^(3)-39x^(2)+36 x Answer:

Identify Common Factor: First, we look for a common factor in all three terms of the polynomial 3x^3 - 39x^2 + 36x. We can see that each term has a factor of 3x, so we factor out 3x from each term. 3x(x^2 - 13x + 12)Factor Quadratic Expression: Now we need to factor the quadratic expression x^2 - 13x + 12. We look for two numbers that multiply to 12 (the constant term) and add up to -13 (the coefficient of the x term). The numbers that satisfy these conditions are -3 and -4, since (-3) * (-4) = 12 and (-3) + (-4) = -7. Therefore, we can factor the quadratic as (x - 3)(x - 4). 3x(x - 3)(x - 4)Check Factoring and Correct Mistake: We check our factoring by expanding the factors to see if we get the original polynomial. 3x(x - 3)(x - 4) = 3x(x^2 - 4x - 3x + 12) = 3x(x^2 - 7x + 12) Expanding further, we get 3x^3 - 21x^2 + 36x, which is not the original polynomial. We made a mistake in the previous step; the correct numbers should add up to -13, not -7.

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Q. Factor completely.

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3 x^{3}-39 x^{2}+36 x

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Answer:

Identify Common Factor: First, we look for a common factor in all three terms of the polynomial $3x^3 - 39x^2 + 36x$ . We can see that each term has a factor of $3x$ , so we factor out $3x$ from each term. $3x(x^2 - 13x + 12)$
Factor Quadratic Expression: Now we need to factor the quadratic expression $x^2 - 13x + 12$ . We look for two numbers that multiply to $12$ (the constant term) and add up to $-13$ (the coefficient of the $x$ term). $\newline$ The numbers that satisfy these conditions are $-3$ and $-4$ , since $(-3) \times (-4) = 12$ and $(-3) + (-4) = -7$ . $\newline$ Therefore, we can factor the quadratic as $(x - 3)(x - 4)$ . $\newline$ $3x(x - 3)(x - 4)$
Check Factoring and Correct Mistake: We check our factoring by expanding the factors to see if we get the original polynomial. $\newline$ $3x(x - 3)(x - 4) = 3x(x^2 - 4x - 3x + 12) = 3x(x^2 - 7x + 12)$ $\newline$ Expanding further, we get $3x^3 - 21x^2 + 36x$ , which is not the original polynomial. $\newline$ We made a mistake in the previous step; the correct numbers should add up to $-13$ , not $-7$ .