Factor. w^3 - w^2 + 7w - 7 ______

Identify Common Factors: Look for common factors in pairs of terms. We can try to factor by grouping, which involves combining terms that have common factors. We'll look at the first two terms and the last two terms separately. First pair: w^3 - w^2 Second pair: 7w - 7Factor by Grouping: Factor out the common factor from the first pair of terms. The common factor in w^3 and w^2 is w^2. w^3 - w^2 = w^2(w - 1)Factor First Pair: Factor out the common factor from the second pair of terms. The common factor in 7w and -7 is 7. 7w - 7 = 7(w - 1)Factor Second Pair: Combine the factored pairs. Now we have: w^2(w - 1) + 7(w - 1) Notice that (w - 1) is a common factor.Combine Factored Pairs: Factor out the common factor (w - 1). We can now factor (w - 1) out of both terms. w^2(w - 1) + 7(w - 1) = (w - 1)(w^2 + 7)

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Algebra 1

Factor by grouping

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Q. Factor.

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w^3 - w^2 + 7w - 7

Identify Common Factors: Look for common factors in pairs of terms. We can try to factor by grouping, which involves combining terms that have common factors. We'll look at the first two terms and the last two terms separately. First pair: $w^3 - w^2$ Second pair: $7w - 7$
Factor by Grouping: Factor out the common factor from the first pair of terms. $\newline$ The common factor in $w^3$ and $w^2$ is $w^2$ . $\newline$ $w^3 - w^2 = w^2(w - 1)$
Factor First Pair: Factor out the common factor from the second pair of terms. $\newline$ The common factor in $7w$ and $-7$ is $7$ . $\newline$ $7w - 7 = 7(w - 1)$
Factor Second Pair: Combine the factored pairs. $\newline$ Now we have: $\newline$ $w^2(w - 1) + 7(w - 1)$ $\newline$ Notice that $(w - 1)$ is a common factor.
Combine Factored Pairs: Factor out the common factor $(w - 1)$ . $\newline$ We can now factor $(w - 1)$ out of both terms. $\newline$ $w^2(w - 1) + 7(w - 1) = (w - 1)(w^2 + 7)$