Factor. 2m^2 - 13m + 11 ______

Identify a, b, c: Identify a, b, and c in the quadratic expression 2m^2 - 13m + 11. Compare 2m^2 - 13m + 11 with ax^2 + bx + c. a = 2 b = -13 c = 11Find two numbers: Find two numbers whose product is a*c (2*11 = 22) and whose sum is b (-13). We need to find two numbers that multiply to 22 and add up to -13. After checking possible factors of 22, we find that -11 and -2 satisfy the conditions. -11 * -2 = 22 -11 + -2 = -13Rewrite middle term: Rewrite the middle term -13m using the two numbers found in Step 2. 2m^2 - 13m + 11 can be rewritten as 2m^2 - 11m - 2m + 11.Factor by grouping: Factor by grouping. Group the terms: (2m^2 - 11m) + (-2m + 11). Factor out the common factors from each group. From the first group, we can factor out m: m(2m - 11). From the second group, we can factor out -1: -1(2m - 11).Factor out common binomial: Factor out the common binomial. We now have m(2m - 11) - 1(2m - 11). The common binomial is (2m - 11). Factor this out to get (2m - 11)(m - 1).

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Factor. $\newline$ $2m^2 - 13m + 11$

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Q. Factor.

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2m^2 - 13m + 11

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $2m^2 - 13m + 11$ . Compare $2m^2 - 13m + 11$ with $ax^2 + bx + c$ . $a = 2$ $b$ $0$ $b$ $1$
Find two numbers: Find two numbers whose product is $a*c$ ( $2*11 = 22$ ) and whose sum is $b$ ( $-13$ ). $\newline$ We need to find two numbers that multiply to $22$ and add up to $-13$ . $\newline$ After checking possible factors of $22$ , we find that $-11$ and $-2$ satisfy the conditions. $\newline$ $-11 * -2 = 22$ $\newline$ $2*11 = 22$ $0$
Rewrite middle term: Rewrite the middle term $-13m$ using the two numbers found in Step $2$ . $\newline$ $2m^2 - 13m + 11$ can be rewritten as $2m^2 - 11m - 2m + 11$ .
Factor by grouping: Factor by grouping. $\newline$ Group the terms: $2m^2 - 11m$ + $-2m + 11$ . $\newline$ Factor out the common factors from each group. $\newline$ From the first group, we can factor out $m$ : $m(2m - 11)$ . $\newline$ From the second group, we can factor out $-1$ : $-1(2m - 11)$ .
Factor out common binomial: Factor out the common binomial. $\newline$ We now have $m(2m - 11) - 1(2m - 11)$ . $\newline$ The common binomial is $(2m - 11)$ . $\newline$ Factor this out to get $(2m - 11)(m - 1)$ .