Factor. 12z^3 - 16z^2 + 3z - 4 ______

Identify Common Factors: Look for common factors in pairs of terms. We will group the terms into two pairs and look for common factors in each pair. Group 1: 12z^3 and -16z^2. Group 2: 3z and -4.Factor Out Common Factors: Factor out the greatest common factor from each group. For Group 1, the greatest common factor is 4z^2. For Group 2, there is no common factor other than 1. So we have: Group 1: 4z^2(3z - 4) Group 2: 3z - 4Check Parentheses: Check if the terms in parentheses are the same for both groups. We notice that both groups have the same term in parentheses, which is (3z - 4).Factor by Grouping: Factor by grouping. Since both groups contain the factor (3z - 4), we can factor it out: (4z^2 + 1)(3z - 4)

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Factor by grouping

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Q. Factor.

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12z^3 - 16z^2 + 3z - 4

Identify Common Factors: Look for common factors in pairs of terms. We will group the terms into two pairs and look for common factors in each pair. Group $1$ : $12z^3$ and $-16z^2$ . Group $2$ : $3z$ and $-4$ .
Factor Out Common Factors: Factor out the greatest common factor from each group. $\newline$ For Group $1$ , the greatest common factor is $4z^2$ . $\newline$ For Group $2$ , there is no common factor other than $1$ . $\newline$ So we have: $\newline$ Group $1$ : $4z^2(3z - 4)$ $\newline$ Group $2$ : $3z - 4$
Check Parentheses: Check if the terms in parentheses are the same for both groups. $\newline$ We notice that both groups have the same term in parentheses, which is $(3z - 4)$ .
Factor by Grouping: Factor by grouping. $\newline$ Since both groups contain the factor $(3z - 4)$ , we can factor it out: $\newline$ $(4z^2 + 1)(3z - 4)$