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 two numbers: 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 -2 and -3 work because: -2 * -3 = 6 -2 + -3 = -5Rewrite middle term: Rewrite the middle term -5x using the two numbers found in Step 2. 3x^2 - 5x + 2 can be rewritten as: 3x^2 - 2x - 3x + 2Factor by grouping: Factor by grouping. Group the terms as follows: (3x^2 - 2x) + (-3x + 2) Factor out the common factors from each group. x(3x - 2) - 1(3x - 2)Factor out common binomial: Factor out the common binomial factor. The common binomial factor is (3x - 2). The factored form is (x - 1)(3x - 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 two numbers: 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 $-2$ and $-3$ work because: $\newline$ $-2 \times -3 = 6$ $\newline$ $-2 + -3 = -5$
Rewrite middle term: Rewrite the middle term $-5x$ using the two numbers found in Step $2$ . $\newline$ $3x^2 - 5x + 2$ can be rewritten as: $\newline$ $3x^2 - 2x - 3x + 2$
Factor by grouping: Factor by grouping. $\newline$ Group the terms as follows: $3x^2 - 2x$ + $-3x + 2$ $\newline$ Factor out the common factors from each group. $\newline$ $x(3x - 2) - 1(3x - 2)$
Factor out common binomial: Factor out the common binomial factor. $\newline$ The common binomial factor is $(3x - 2)$ . $\newline$ The factored form is $(x - 1)(3x - 2)$ .