Question

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

Answer 1

C. (x² + 12)(x + 2)

Step-by-step explanation

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

`(x^3+2x^2)+(12x+24)`

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,

`x^2(x+2)+12(x+2)`

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

`(x^2+12)(x+2)`

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