Factor. 3k^2 - 8k + 5 ______

Identify a, b, c: Identify a, b, and c in the quadratic expression 3k^2 - 8k + 5. Compare 3k^2 - 8k + 5 with ax^2 + bx + c. a = 3 b = -8 c = 5Find two numbers: Find two numbers whose product is a*c (3*5 = 15) and whose sum is b (-8). We need to find two numbers that multiply to 15 and add up to -8. The numbers -3 and -5 work because: -3 * -5 = 15 -3 + -5 = -8Rewrite middle term: Rewrite the middle term -8k using the two numbers found in Step 2. 3k^2 - 8k + 5 can be rewritten as 3k^2 - 3k - 5k + 5.Factor by grouping: Factor by grouping. Group the terms: (3k^2 - 3k) + (-5k + 5). Factor out the common factors from each group. 3k(k - 1) - 5(k - 1).Factor out common binomial: Factor out the common binomial factor (k - 1). (3k - 5)(k - 1) is the factored form of 3k^2 - 8k + 5.

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3k^2 - 8k + 5

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $3k^2 - 8k + 5$ . Compare $3k^2 - 8k + 5$ with $ax^2 + bx + c$ . $a = 3$ $b$ $0$ $b$ $1$
Find two numbers: Find two numbers whose product is $a*c$ ( $3*5 = 15$ ) and whose sum is $b$ ( $-8$ ). $\newline$ We need to find two numbers that multiply to $15$ and add up to $-8$ . $\newline$ The numbers $-3$ and $-5$ work because: $\newline$ $-3 * -5 = 15$ $\newline$ $-3 + -5 = -8$
Rewrite middle term: Rewrite the middle term $-8k$ using the two numbers found in Step $2$ . $3k^2 - 8k + 5$ can be rewritten as $3k^2 - 3k - 5k + 5$ .
Factor by grouping: Factor by grouping. $\newline$ Group the terms: $(3k^2 - 3k) + (-5k + 5)$ . $\newline$ Factor out the common factors from each group. $\newline$ $3k(k - 1) - 5(k - 1)$ .
Factor out common binomial: Factor out the common binomial factor $(k - 1)$ . $(3k - 5)(k - 1)$ is the factored form of $3k^2 - 8k + 5$ .