12. the expression $(x^{2}+2)-33+(4 - x)$ simplifies to\na) $x^{2}-2x + 13$\nb) $x^{2}+11x - 8$\nc)…

12. the expression $(x^{2}+2)-33+(4 - x)$ simplifies to\na) $x^{2}-2x + 13$\nb) $x^{2}+11x - 8$\nc) $2x^{3}-5x^{2}+11x - 1$\nd) $x^{2}+3x - 19$

12. the expression $(x^{2}+2)-33+(4 - x)$ simplifies to\na) $x^{2}-2x + 13$\nb) $x^{2}+11x - 8$\nc) $2x^{3}-5x^{2}+11x - 1$\nd) $x^{2}+3x - 19$

Answer

Explanation:

Step1: Simplify the inner - bracket

First, simplify (3+(4 - x)=3 + 4-x=7 - x).

Step2: Simplify the outer - bracket

Then, (3[7 - x]=21-3x).

Step3: Expand the entire expression

Now, ((x^{2}+2)-3[3+(4 - x)]=(x^{2}+2)-(21 - 3x)). Using the distributive property (a-(b - c)=a - b + c), we get (x^{2}+2-21 + 3x).

Step4: Combine like terms

Combine the constant terms (2-21=-19). So the expression is (x^{2}+3x-19).

Answer:

D. (x^{2}+3x - 19)