Simplify the expression:
\$ 2(x + 3) + 5x - (x^2 - 2x) \$

A) \$ 9x + 3 − x^2 \$

B) \$ 9x + 6 − x^2 \$

C) \$ 3x + 6 − x^2 \$

D) \$ 3x + 6 − 8x^2 \$

A rectangular garden has a length that is 3 meters longer than its width. Write two equivalent expressions for the garden’s perimeter (p for perimeter, w for width).

A) \$ p = 2w + 6, p = 2(w + 3) + w \$

B) \$ p = 4w + 1, p = 2(w + 1) + 2w \$

C) \$ p = 4w + 6, p = 2(w + 3) + 2w \$

D) \$ p = 4w + 8, p = (w + 3) + 2w \$

Simplify the equivalent expression \$ ((x^2 - 4) / (x - 2)) + ((2x + 3) / (x + 1)) \$.

A) \$ (2x^3 + 3x^2 − 7x + 2​) / (x^2 − x − 2) \$

B) \$ (x^3 + 3x^2 − 7x + 2​) / (4x^2 − x − 2) \$

C) \$ (x^3 + 3x^2 − 7x + 2​) / (x^2 − 6x − 2) \$

D) \$ (x^3 + 3x^2 − 7x + 2​) / (x^2 − x − 2) \$

Find the values of x that make the following expressions equivalent:
\$ -(x^2 - x - 2) / (x + 2) < 0 \$

A) \$ −2 < x < −1 and x > 2 \$

B) \$ −1 < x < −1 and x > 2 \$

C) \$ −2 < x < −4 and x > 2 \$

D) \$ −2 < x < −3 and x > -2 \$

Simplify the expression:
\$ ((2x + 1)/(x - 2)) + ((x - 3)/(x + 2)) \$

A) \$ (3x^2 + 8​)/(x^2 − 4) \$

B) \$ (3x^2 + 8​)/(x^2 − 2) \$

C) \$ (3x^2 + 7)/(x^2 − 4) \$

D) \$ (x^2 + 3​)/(x^2 − 3) \$

If b and d are positive numbers, which of the following is equivalent to \$\sqrt((b + d)^2)\$. \$\sqrt((b + d))\$?

A) \$(b + d)^4\$

B) b + d

C) \$(b + d)^2\$

D) \$(b - d)^4\$

Which of the following expressions is equivalent to \$4(x^2 - 3x + 2)\$.

A) \$4(x^2 - 12x + 8)\$

B) \$4(x^2 + 12x + 2)\$

C) \$4(x^2 - 6x + 8)\$

D) \$4(x^2 + 6x + 4)\$

Two workers, C and D, can complete a painting job together in 8 hours. Worker C alone can complete the job in 12 hours. Write an expression for the time it takes worker D to complete the job alone, and solve for it.

A) 20 hrs

B) 24 hrs

C) 28 hrs

D) 18 hrs

Simplify the expression:
\$3^(2x + 1) times 9^(3 - x) / 27^(x - 1)\$

A)\$3^(10 + 2x)\$

B) \$3^(3 - 10x)\$

C) \$3^(10 - 3x)\$

D) \$3^(4 + 10x)\$

Simplify the expression:
\$(2x^2 - 3x + 1)(x^3 + 4x^2 - 2x + 3) - 2x(x^2 - 1)(x - 2)\$

A) \$2x^5 - 3x^4 - 11x^3 - 18x^2 + 15x + 3\$

B) \$2x^5 + 3x^4 + 11x^3 + 18x^2 - 15x + 3\$

C) \$2x^5 - 3x^4 - 11x^3 + 18x^2 - 15x + 3\$

D) \$2x^5 + 3x^4 - 11x^3 + 18x^2 - 15x + 3\$