Factor. 18y^3 + 9y^2 - 20y - 10 ______

Group Terms: Group the terms to find common factors. Group the first two terms and the last two terms separately. 18y^3 + 9y^2 - 20y - 10 can be written as (18y^3 + 9y^2) - (20y + 10).Factor Common Factors: Factor out the greatest common factor from each group. From the first group (18y^3 + 9y^2), we can factor out 9y^2, which gives us 9y^2(2y + 1). From the second group (20y + 10), we can factor out 10, which gives us 10(2y + 1). Now we have 9y^2(2y + 1) - 10(2y + 1).Factor Greatest Common Factor: Factor out the common binomial factor. Both groups now have a common factor of (2y + 1). Factor out (2y + 1) from both groups. The expression becomes (2y + 1)(9y^2 - 10).Factor Common Binomial: Check if the quadratic can be factored further. The quadratic 9y^2 - 10 does not factor nicely with integer coefficients, so it is already in its simplest form.

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Q. Factor.

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18y^3 + 9y^2 - 20y - 10

Group Terms: Group the terms to find common factors. $\newline$ Group the first two terms and the last two terms separately. $\newline$ $18y^3 + 9y^2 - 20y - 10$ can be written as $(18y^3 + 9y^2) - (20y + 10)$ .
Factor Common Factors: Factor out the greatest common factor from each group. $\newline$ From the first group $18y^3 + 9y^2$ , we can factor out $9y^2$ , which gives us $9y^2(2y + 1)$ . $\newline$ From the second group $20y + 10$ , we can factor out $10$ , which gives us $10(2y + 1)$ . $\newline$ Now we have $9y^2(2y + 1) - 10(2y + 1)$ .
Factor Greatest Common Factor: Factor out the common binomial factor. $\newline$ Both groups now have a common factor of $(2y + 1)$ . $\newline$ Factor out $(2y + 1)$ from both groups. $\newline$ The expression becomes $(2y + 1)(9y^2 - 10)$ .
Factor Common Binomial: Check if the quadratic can be factored further. $\newline$ The quadratic $9y^2 - 10$ does not factor nicely with integer coefficients, so it is already in its simplest form.