Factor completely. 2x^(2)-3x+1 Answer:

Identify a, b, c: Identify a, b, and c in the quadratic expression 2x^2 - 3x + 1. Compare 2x^2 - 3x + 1 with ax^2 + bx + c. a = 2 b = -3 c = 1Find product and sum: Find two numbers whose product is a*c (2*1 = 2) and whose sum is b (-3). We need to find two numbers that multiply to 2 and add up to -3. The numbers -1 and -2 satisfy these conditions because: -1 * -2 = 2 -1 + -2 = -3Rewrite middle term: Rewrite the middle term -3x using the two numbers found in Step 2. 2x^2 - 3x + 1 can be rewritten as: 2x^2 - x - 2x + 1Factor by grouping: Factor by grouping. Group the terms into two pairs: (2x^2 - x) + (-2x + 1) Factor out the greatest common factor from each pair: x(2x - 1) - 1(2x - 1)Factor out common binomial: Factor out the common binomial factor. The common binomial factor is (2x - 1), so we factor it out: (2x - 1)(x - 1)

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Q. Factor completely.

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2 x^{2}-3 x+1

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Answer:

Identify $a, b, c$ : Identify $a, b,$ and $c$ in the quadratic expression $2x^2 - 3x + 1$ . Compare $2x^2 - 3x + 1$ with $ax^2 + bx + c$ . $a = 2$ $b = -3$ $c = 1$
Find product and sum: Find two numbers whose product is $a*c$ ( $2*1 = 2$ ) and whose sum is $b$ ( $-3$ ). $\newline$ We need to find two numbers that multiply to $2$ and add up to $-3$ . $\newline$ The numbers $-1$ and $-2$ satisfy these conditions because: $\newline$ $-1 * -2 = 2$ $\newline$ $-1 + -2 = -3$
Rewrite middle term: Rewrite the middle term $-3x$ using the two numbers found in Step $2$ . $\newline$ $2x^2 - 3x + 1$ can be rewritten as: $\newline$ $2x^2 - x - 2x + 1$
Factor by grouping: Factor by grouping. $\newline$ Group the terms into two pairs: $\newline$ $(2x^2 - x) + (-2x + 1)$ $\newline$ Factor out the greatest common factor from each pair: $\newline$ $x(2x - 1) - 1(2x - 1)$
Factor out common binomial: Factor out the common binomial factor. $\newline$ The common binomial factor is $(2x - 1)$ , so we factor it out: $\newline$ $(2x - 1)(x - 1)$