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

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

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

Answer

Explanation:

Step1: Group the terms

Group the polynomial (x^{3}-9x^{2}+5x - 45) into two - groups: ((x^{3}-9x^{2})+(5x - 45)).

Step2: Factor out the GCF from each group

From the first group (x^{3}-9x^{2}), the greatest - common factor (GCF) is (x^{2}), so (x^{3}-9x^{2}=x^{2}(x - 9)). From the second group (5x - 45), the GCF is 5, so (5x - 45 = 5(x - 9)). Then the polynomial becomes (x^{2}(x - 9)+5(x - 9)). This is not in the options. Let's group it in another way: ((x^{3}+5x)+(-9x^{2}-45)).

Step3: Factor out the GCF from each new - group

From the first group (x^{3}+5x), the GCF is (x), so (x^{3}+5x=x(x^{2}+5)). From the second group (-9x^{2}-45), the GCF is (-9), so (-9x^{2}-45=-9(x^{2}+5)).

Step4: Combine the factored forms

The factored form of the polynomial (x^{3}-9x^{2}+5x - 45) by grouping is (x(x^{2}+5)-9(x^{2}+5)).

Answer:

C. (x(x^{2}+5)-9(x^{2}+5))