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Use the grouping method to factor this polynomial[tex] {x}^{3} + 2 {x}^{2} + 12x + 24[/tex]A. (x²+6)(x+2)B. (x²+2)(x+6)OC. (x²+12)(x+2)D. (x²+2)(x+12)

Answer :

ANSWER

C. (x² + 12)(x + 2)

EXPLANATION

To factor this polynomial using the grouping method, first, we have to group the first two and the last two terms,

[tex](x^3+2x^2)+(12x+24)[/tex]

Note that x² is a common factor of the first group while 12 is a common factor of the second group, so let's factor those out,

[tex]x^2(x+2)+12(x+2)[/tex]

As we can see, both terms have also a common factor, (x + 2), so when factoring it out, we get the factored expression,

[tex](x^2+12)(x+2)[/tex]

Hence, the factored polynomial is (x² + 12)(x + 2).

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