Answered

Get expert advice and community support for all your questions on IDNLearn.com. Join our community to receive prompt and reliable responses to your questions from experienced professionals.

Which shows one way to determine the factors of [tex]$x^3+5x^2-6x-30$[/tex] by grouping?

A. [tex]x\left(x^2-5\right)+6\left(x^2-5\right)[/tex]
B. [tex]x\left(x^2+5\right)-6\left(x^2+5\right)[/tex]
C. [tex]x^2(x-5)+6(x-5)[/tex]
D. [tex]x^2(x+5)-6(x+5)[/tex]

Sagot :

GinnyAnsweridn
To determine the factors of the polynomial [tex]\( x^3 + 5x^2 - 6x - 30 \)[/tex] by grouping, follow these steps:

1. Group the terms: The given polynomial is [tex]\( x^3 + 5x^2 - 6x - 30 \)[/tex]. We want to group terms in pairs that can be factored easily.

[tex]\[ (x^3 + 5x^2) + (-6x - 30) \][/tex]

2. Factor out the common factors in each group:

- For the first group [tex]\( x^3 + 5x^2 \)[/tex], the common factor is [tex]\( x^2 \)[/tex]:

[tex]\[ x^2 (x + 5) \][/tex]

- For the second group [tex]\( -6x - 30 \)[/tex], the common factor is [tex]\(-6\)[/tex]:

[tex]\[ -6(x + 5) \][/tex]

3. Write the expression after factoring out the common factors:

[tex]\[ x^2 (x + 5) - 6 (x + 5) \][/tex]

4. Factor out the common binomial factor [tex]\((x + 5)\)[/tex]:

[tex]\[ (x^2 - 6)(x + 5) \][/tex]

Therefore, the correct way to factor [tex]\( x^3 + 5x^2 - 6x - 30 \)[/tex] by grouping is:
[tex]\[ x^2 (x + 5) - 6 (x + 5) \][/tex]

This corresponds to the option:
[tex]\[ x^2 (x + 5) - 6 (x + 5) \][/tex]

So, the correct choice is:
[tex]\[ x^2 (x + 5) - 6 (x + 5) \][/tex]
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Discover the answers you need at IDNLearn.com. Thanks for visiting, and come back soon for more valuable insights.