Mathematics

Question

which expression is equal to (x+2) (-x^2+2x-6)
A: -x^3-4x^2-2x-12
B: -x^3-4x^2-10x-12
C: -x^3-2x-12
D: -x^3-10x-12

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  • Answer:

    [tex]\huge\boxed{C.\ -x^3-2x-12}[/tex]

    Step-by-step explanation:

    [tex](x+2)(-x^2+2x-6)\\\\=(x)(-x^2)+(x)(2x)+(x)(-6)+(2)(-x^2)+(2)(2x)+(2)(-6)\\\\=-x^3+2x^2-6x-2x^2+4x-12\\\\\text{combine like terms}\\\\=-x^3+(2x^2-2x^2)+(-6x+4x)-12\\\\=-x^3-2x-12[/tex]