Factor. 7u^3 - 14u^2 - 5u + 10 ______

Question

Bytelearn · Accepted Answer

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: 7u^3 - 14u^2 Second pair: -5u + 10Factor by Grouping: Factor out the greatest common factor from the first pair of terms. The greatest common factor of 7u^3 and 14u^2 is 7u^2. 7u^3 - 14u^2 = 7u^2(u - 2)Factor First Pair: Factor out the greatest common factor from the second pair of terms. The greatest common factor of -5u and 10 is 5. -5u + 10 = 5(-u + 2) Notice that we factored out a positive 5, which makes the second term in the parentheses negative to match the original expression.Factor Second Pair: Rewrite the original expression using the factored pairs. 7u^3 - 14u^2 - 5u + 10 = 7u^2(u - 2) + 5(-u + 2)Rewrite Using Factored Pairs: Look for a common binomial factor in the two new terms. We can see that the binomials (u - 2) and (-u + 2) are not the same, but (-u + 2) is the negative of (u - 2). We can factor out -1 from the second term to make the binomials match. 7u^2(u - 2) + 5(-u + 2) = 7u^2(u - 2) - 5(u - 2)Identify Common Binomial Factor: Factor out the common binomial factor. Now that we have a common binomial factor of (u - 2), we can factor it out. 7u^3 - 14u^2 - 5u + 10 = (u - 2)(7u^2 - 5)

Factor. $\newline$ $7u^3 - 14u^2 - 5u + 10$

Full solution

More problems from Factor by grouping

Related topics

Factor.\newline7u3−14u2−5u+107u^3 - 14u^2 - 5u + 107u3−14u2−5u+10

Factor. $\newline$ $7u^3 - 14u^2 - 5u + 10$