Question

which shows one way to determine the factors of ( x^3 - 9x^2 + 5x - 45 ) by grouping?
( \bigcirc x^2(x - 9) + 5(x - 9) )
( \bigcirc x^2(x + 9) + 5(x + 9) )
( \bigcirc x(x^2 + 5) - 9(x^2 + 5) )
( \bigcirc x(x^2 - 5) - 9(x^2 - 5) )

Explanation:

Step1: Group polynomial terms

Group into two pairs: $(x^3 - 9x^2) + (5x - 45)$

Step2: Factor out GCF from each group

Factor $x^2$ from first pair, 5 from second: $x^2(x - 9) + 5(x - 9)$

Step3: Match to given options

Compare with the provided choices to find the match.

Answer:

$x^2(x - 9) + 5(x - 9)$ (the first option)