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Factor. $\newline$ $10z^3 - 5z^2 + 18z - 9$

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Factor by grouping

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Q. Factor.

\newline

10z^3 - 5z^2 + 18z - 9

Factorize cubic polynomial: Write the factored form of $10z^3 - 5z^2$ . Factor out $5z^2$ from $10z^3$ and $5z^2$ . $10z^3 - 5z^2 = 5z^2(2z - 1)$
Factorize linear polynomial: Write the factored form of $18z - 9$ . $\newline$ Factor out $9$ from $18z$ and $9$ . $\newline$ $18z - 9 = 9(2z - 1)$
Combine factorized polynomials: We found: $\newline$ $10z^3 - 5z^2 = 5z^2(2z - 1)$ $\newline$ $18z - 9 = 9(2z - 1)$ $\newline$ Write the factored form of $10z^3 - 5z^2 + 18z - 9$ . $\newline$ Factor out $(2z - 1)$ from $5z^2(2z - 1)$ and $9(2z - 1)$ . $\newline$ So, the factored form of $10z^3 - 5z^2 + 18z - 9$ is: $(5z^2 + 9)(2z - 1)$

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