Factor completely. 3x^(2)-5x-2 Answer:

Identify a, b, c: Identify a, b, and c in the quadratic expression 3x^2 - 5x - 2. Compare 3x^2 - 5x - 2 with ax^2 + bx + c. a = 3 b = -5 c = -2Find product and sum: Find two numbers whose product is a*c (3*-2 = -6) and whose sum is b (-5). We need to find two numbers that multiply to -6 and add up to -5. The numbers -6 and 1 satisfy these conditions because: -6 * 1 = -6 (product) -6 + 1 = -5 (sum)Rewrite middle term: Rewrite the middle term -5x using the two numbers found in Step 2. 3x^2 - 5x - 2 becomes 3x^2 - 6x + x - 2.Factor by grouping: Factor by grouping. Group the terms: (3x^2 - 6x) + (x - 2). Factor out the common factors from each group. From the first group, factor out 3x: 3x(x - 2). From the second group, factor out 1: 1(x - 2). Now we have: 3x(x - 2) + 1(x - 2).Factor out common factor: Factor out the common binomial factor (x - 2). The factored form is (3x + 1)(x - 2).

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Q. Factor completely.

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3 x^{2}-5 x-2

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Answer:

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $3x^2 - 5x - 2$ . Compare $3x^2 - 5x - 2$ with $ax^2 + bx + c$ . $a = 3$ $b$ $0$ $b$ $1$
Find product and sum: Find two numbers whose product is $a*c$ ( $3*-2 = -6$ ) and whose sum is $b$ ( $-5$ ). $\newline$ We need to find two numbers that multiply to $-6$ and add up to $-5$ . $\newline$ The numbers $-6$ and $1$ satisfy these conditions because: $\newline$ $-6 * 1 = -6$ (product) $\newline$ $-6 + 1 = -5$ (sum)
Rewrite middle term: Rewrite the middle term $-5x$ using the two numbers found in Step $2$ . $\newline$ $3x^2 - 5x - 2$ becomes $3x^2 - 6x + x - 2$ .
Factor by grouping: Factor by grouping. $\newline$ Group the terms: $(3x^2 - 6x) + (x - 2)$ . $\newline$ Factor out the common factors from each group. $\newline$ From the first group, factor out $3x$ : $3x(x - 2)$ . $\newline$ From the second group, factor out $1$ : $1(x - 2)$ . $\newline$ Now we have: $3x(x - 2) + 1(x - 2)$ .
Factor out common factor: Factor out the common binomial factor $(x - 2)$ . $\newline$ The factored form is $(3x + 1)(x - 2)$ .