which shows one way to determine the factors of x³ - 9x² + 5x - 45 by grouping?\n○ x²(x - 9) - 5(x - 9)\n○…

which shows one way to determine the factors of x³ - 9x² + 5x - 45 by grouping?\n○ x²(x - 9) - 5(x - 9)\n○ x²(x + 9) - 5(x + 9)\n○ x(x² + 5) - 9(x² + 5)\n○ x(x² - 5) - 9(x² - 5)

which shows one way to determine the factors of x³ - 9x² + 5x - 45 by grouping?\n○ x²(x - 9) - 5(x - 9)\n○ x²(x + 9) - 5(x + 9)\n○ x(x² + 5) - 9(x² + 5)\n○ x(x² - 5) - 9(x² - 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 greatest common factor from each group

From the first group $x^{3}-9x^{2}$, the 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 equivalent to $x^{2}(x - 9)-(- 5)(x - 9)$. Another way is to group it as $(x^{3}+5x)-(9x^{2}+45)$. Factor out the GCF from each group: from $x^{3}+5x$, the GCF is $x$, so $x^{3}+5x=x(x^{2}+5)$; from $9x^{2}+45$, the GCF is 9, so $9x^{2}+45 = 9(x^{2}+5)$. Then the polynomial is $x(x^{2}+5)-9(x^{2}+5)$.

Answer:

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