Factor. 2f^2 - 7f + 6 ______

Identify a, b, c: Identify a, b, and c in the quadratic expression 2f^2 - 7f + 6. Compare 2f^2 - 7f + 6 with ax^2 + bx + c. a = 2 b = -7 c = 6Find two numbers: Find two numbers whose product is a*c (2*6 = 12) and whose sum is b (-7). We need to find two numbers that multiply to 12 and add up to -7. -3 * -4 = 12 -3 + -4 = -7 Two numbers: -3, -4Rewrite middle term: Rewrite the middle term -7f using the two numbers found in Step 2. 2f^2 - 7f + 6 can be rewritten as 2f^2 - 3f - 4f + 6.Factor by grouping: Factor by grouping. Group the terms: (2f^2 - 3f) + (-4f + 6). Factor out the common factors from each group. f(2f - 3) - 2(2f - 3).Factor common binomial: Factor out the common binomial factor. The common binomial factor is (2f - 3). The factored form is (f - 2)(2f - 3).

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2f^2 - 7f + 6

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $2f^2 - 7f + 6$ . Compare $2f^2 - 7f + 6$ with $ax^2 + bx + c$ . $a = 2$ $b$ $0$ $b$ $1$
Find two numbers: Find two numbers whose product is $a*c$ ( $2*6 = 12$ ) and whose sum is $b$ ( $-7$ ). $\newline$ We need to find two numbers that multiply to $12$ and add up to $-7$ . $\newline$ $-3 * -4 = 12$ $\newline$ $-3 + -4 = -7$ $\newline$ Two numbers: $-3$ , $-4$
Rewrite middle term: Rewrite the middle term $-7f$ using the two numbers found in Step $2$ . $2f^2 - 7f + 6$ can be rewritten as $2f^2 - 3f - 4f + 6$ .
Factor by grouping: Factor by grouping. $\newline$ Group the terms: $2f^2 - 3f$ + $-4f + 6$ . $\newline$ Factor out the common factors from each group. $\newline$ $f(2f - 3) - 2(2f - 3)$ .
Factor common binomial: Factor out the common binomial factor. $\newline$ The common binomial factor is $(2f - 3)$ . $\newline$ The factored form is $(f - 2)(2f - 3)$ .