Factor. 6t^3 - 12t^2 + 7t - 14 ______

Identify Common Factors: Look for common factors in each pair of terms. We can factor by grouping. First, we look at the first two terms 6t^3 and -12t^2 and factor out the greatest common factor, which is 6t^2. 6t^3 - 12t^2 = 6t^2(t - 2)Factor by Grouping: Look for common factors in the last pair of terms. Now, we look at the last two terms 7t and -14 and factor out the greatest common factor, which is 7. 7t - 14 = 7(t - 2)Factor Last Pair: Write the expression with the factored groups. We now have: 6t^3 - 12t^2 + 7t - 14 = 6t^2(t - 2) + 7(t - 2)Write Factored Expression: Factor out the common binomial factor. We can see that (t - 2) is a common factor in both terms. 6t^3 - 12t^2 + 7t - 14 = (6t^2 + 7)(t - 2)

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Math Problems

Algebra 1

Factor by grouping

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Q. Factor.

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6t^3 - 12t^2 + 7t - 14

Identify Common Factors: Look for common factors in each pair of terms. $\newline$ We can factor by grouping. First, we look at the first two terms $6t^3$ and $-12t^2$ and factor out the greatest common factor, which is $6t^2$ . $\newline$ $6t^3 - 12t^2 = 6t^2(t - 2)$
Factor by Grouping: Look for common factors in the last pair of terms. $\newline$ Now, we look at the last two terms $7t$ and $-14$ and factor out the greatest common factor, which is $7$ . $\newline$ $7t - 14 = 7(t - 2)$
Factor Last Pair: Write the expression with the factored groups. $\newline$ We now have: $\newline$ $6t^3 - 12t^2 + 7t - 14 = 6t^2(t - 2) + 7(t - 2)$
Write Factored Expression: Factor out the common binomial factor. $\newline$ We can see that $(t - 2)$ is a common factor in both terms. $\newline$ $6t^3 - 12t^2 + 7t - 14 = (6t^2 + 7)(t - 2)$