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

Identify Common Factors: Look for common factors in the first two terms and the last two terms separately. For the first two terms, 18t^3 and -9t^2, the common factor is 9t^2. For the last two terms, -20t and +10, the common factor is -10.Factor Out Common Factors: Factor out the common factors from the first two terms and the last two terms. Factoring out 9t^2 from 18t^3 - 9t^2 gives us 9t^2(2t - 1). Factoring out -10 from -20t + 10 gives us -10(2t - 1).Rewrite Polynomial: Rewrite the polynomial with the factored groups. The polynomial now looks like this: 9t^2(2t - 1) - 10(2t - 1).Factor Out Binomial Factor: Factor out the common binomial factor (2t - 1). Both terms have a common binomial factor of (2t - 1), so we can factor that out: (2t - 1)(9t^2 - 10).Check Quadratic Factor: Check if the quadratic factor can be factored further. The quadratic factor 9t^2 - 10 does not factor nicely with integer coefficients, so it is left as is.

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

Identify Common Factors: Look for common factors in the first two terms and the last two terms separately. $\newline$ For the first two terms, $18t^3$ and $-9t^2$ , the common factor is $9t^2$ . $\newline$ For the last two terms, $-20t$ and $+10$ , the common factor is $-10$ .
Factor Out Common Factors: Factor out the common factors from the first two terms and the last two terms. $\newline$ Factoring out $9t^2$ from $18t^3 - 9t^2$ gives us $9t^2(2t - 1)$ . $\newline$ Factoring out $-10$ from $-20t + 10$ gives us $-10(2t - 1)$ .
Rewrite Polynomial: Rewrite the polynomial with the factored groups. $\newline$ The polynomial now looks like this: $9t^2(2t - 1) - 10(2t - 1)$ .
Factor Out Binomial Factor: Factor out the common binomial factor $(2t - 1)$ . $\newline$ Both terms have a common binomial factor of $(2t - 1)$ , so we can factor that out: $\newline$ $(2t - 1)(9t^2 - 10)$ .
Check Quadratic Factor: Check if the quadratic factor can be factored further. $\newline$ The quadratic factor $9t^2 - 10$ does not factor nicely with integer coefficients, so it is left as is.