Solve the quadratic equation by factoring: \$x^2 − 5x + 6\$ = 0.

A) x = 3, 1

B) x = 3, 4

C) x = 2, 4

D) x = 2, 3

The number of shirts sold by the shopkeeper is given by the expression 3x - 5. The price per shirt is given by the expression 2x + 1. Find the total amount of revenue earned by the shopkeeper by selling the shirts.

A) \$x^2 - 7x - 5\$

B) \$6x^2 - 7x - 5\$

C) \$6x^2 - 5x - 5\$

D) \$3x^2 - 7x - 5\$

Solve for x: \$ (3x^2 - 12)/(x^2 - 1) \$ = 2.

A) \$x = ± sqrt1\$

B) \$x = ± sqrt8\$

C) \$x = ± sqrt10\$

D) \$x = ± sqrt20\$

Find the limit of the function
\$f(x) = (3x^2 - 5x + 2) / (2x^2 + 3x - 2)\$ as x approaches 2.

A) \$ 1/3 \$

B) 3

C) \$ 2/3 \$

D) 9

Solve the equation \$(2x^2 - x - 28) / (20 - x - x^2)\$.

A) \$- (2x - 7) / (x - 5)\$

B) \$- (2x + 7) / (x + 5)\$

C) \$- (2x - 7) / (2x + 5)\$

D) \$- (2x + 7) / (2x + 5)\$

Let α, β; α > β, be the roots of the equation \$x^2 - \sqrt2x - \sqrt3 = 0\$. Let \$P_n = α^n - β^n\$, n ∈ N. Then \$(11 \sqrt3 - 10 \sqrt2) P_10 + (11 \sqrt2 + 10) P_11 - 11 P_12\$ is equal to.

A) \$10 \sqrt3 P_9\$

B) \$12 \sqrt5 P_8\$

C) \$15 \sqrt6 P_12\$

D) \$15 \sqrt3 P_9\$

Factor each of the polynomials is \$x^5 - 7x^4 - 2x^3 + 100x^2 - 232x + 160\$.

A) \$(x - 3) (x^4 - x^3 - 11x^2 + 4x - 40)\$

B) \$(x - 3) (x^4 - 3x^3 - 12x^2 + 34x - 40)\$

C) \$ (x - 1)^2(x + 3)(x - 4)\$

D) \$ (x - 2)^3(x + 4)(x - 5)\$

Solve the equation:
\$ 3x^2 + 2x - (1/2) \$ = x

A) \$x = ± sqrt8/3\$

B) \$x = ± sqrt3/5\$

C) \$x = (1 ± sqrt(7))/6\$

D) \$x = (2 ± sqrt1)/3\$

Evaluate the limit: \$lim_(x->∞) (5x^2 - 2x + 1)/(3x^2 + x - 4)\$ =

A) \$4 / 3\$

B) \$5 / 3\$

C) \$5 / 2\$

D) \$2 / 3\$

Suppose \$H(t) = t^2 + 5t + 1\$. Find the limit \$lim_(t->2) H(t)\$.

A) 9

B) 1

C) 2t + 5

D) 15