Factor. 8q^3 - 6q^2 + 20q - 15 ______

Question

Bytelearn · Accepted Answer

Identify Common Factor: Look for a common factor in all terms. Check if there is a greatest common factor (GCF) that can be factored out from all the terms in the polynomial 8q^3 - 6q^2 + 20q - 15. The GCF of 8, -6, 20, and -15 is 1, and since there is no common q factor in all terms, we cannot factor out a GCF other than 1.Group for Factoring: Group terms to factor by grouping. Since there is no common factor, we can try to factor by grouping. Group the first two terms together and the last two terms together: (8q^3 - 6q^2) + (20q - 15) Now, factor out the common factors from each group.Factor Out Common Factors: Factor out the common factors from each group. From the first group (8q^3 - 6q^2), we can factor out 2q^2: 2q^2(4q - 3) From the second group (20q - 15), we can factor out 5: 5(4q - 3) Now we have: 2q^2(4q - 3) + 5(4q - 3)Factor Out Binomial Factor: Factor out the common binomial factor. We can see that (4q - 3) is a common factor in both terms: 2q^2(4q - 3) + 5(4q - 3) Factor out (4q - 3): (4q - 3)(2q^2 + 5)

Factor. $\newline$ $8q^3 - 6q^2 + 20q - 15$

Full solution

More problems from Factor by grouping

Related topics

Factor.\newline8q3−6q2+20q−158q^3 - 6q^2 + 20q - 158q3−6q2+20q−15

Factor. $\newline$ $8q^3 - 6q^2 + 20q - 15$