Factor. 3t^2 - 11t + 6 ______

Identify a, b, c: Identify a, b, and c in the quadratic expression 3t^2 - 11t + 6. Compare 3t^2 - 11t + 6 with at^2 + bt + c. a = 3 b = -11 c = 6Find two numbers: Find two numbers whose product is a*c (3*6 = 18) and whose sum is b (-11). We need to find two numbers that multiply to 18 and add up to -11. -9 * -2 = 18 -9 + -2 = -11 Two numbers: -9, -2Rewrite middle term: Rewrite the middle term -11t using the two numbers found in Step 2. 3t^2 - 9t - 2t + 6 Group the terms to factor by grouping. (3t^2 - 9t) + (-2t + 6)Factor by grouping: Factor out the common factors from each group. 3t(t - 3) - 2(t - 3) Now we have a common binomial factor (t - 3).Factor common factors: Factor out the common binomial factor. (3t - 2)(t - 3) This is the factored form of the quadratic expression.

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3t^2 - 11t + 6

Identify $a$ , $b$ , $c$ : Identify $a$ , $b$ , and $c$ in the quadratic expression $3t^2 - 11t + 6$ . Compare $3t^2 - 11t + 6$ with $at^2 + bt + c$ . $a = 3$ $b$ $0$ $b$ $1$
Find two numbers: Find two numbers whose product is $a*c$ ( $3*6 = 18$ ) and whose sum is $b$ ( $-11$ ). $\newline$ We need to find two numbers that multiply to $18$ and add up to $-11$ . $\newline$ $-9 * -2 = 18$ $\newline$ $-9 + -2 = -11$ $\newline$ Two numbers: $-9$ , $-2$
Rewrite middle term: Rewrite the middle term $-11t$ using the two numbers found in Step $2$ . $\newline$ $3t^2 - 9t - 2t + 6$ $\newline$ Group the terms to factor by grouping. $\newline$ $(3t^2 - 9t) + (-2t + 6)$
Factor by grouping: Factor out the common factors from each group. $\newline$ $3t(t - 3) - 2(t - 3)$ $\newline$ Now we have a common binomial factor $(t - 3)$ .
Factor common factors: Factor out the common binomial factor. $\newline$ $(3t - 2)(t - 3)$ $\newline$ This is the factored form of the quadratic expression.