Exam 1: Review of Basic Concepts

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $( 3 x + 12 ) ( x + 8 )$

Factor the trinomial, if possible. - $162 m ^ { 2 } + 252 m n + 98 n ^ { 2 }$

Solve the problem. - $( n - 12 ) ( n + 12 )$

Use the distributive property to rewrite a sum as a product or the product as a sum. -5(b + r)

Factor by grouping. - $20 x ^ { 6 } - 25 x ^ { 3 } - 12 x ^ { 3 } + 15$

Simplify the expression. Assume all variables represent positive real numbers. - $4 \sqrt [ 3 ] { a } + \sqrt [ 3 ] { 8 a }$

Factor the trinomial, if possible. - $64 m ^ { 2 } + 128 m + 64$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { \frac { 6 } { y } } { \frac { 8 } { y + 9 } }$

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - $\frac { \sqrt { x } - \sqrt { y } } { \sqrt { 6 x } + \sqrt { 7 y } }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\left( \frac { 5 } { 2 } y \right) ( 2 )$

Find the product or quotient. - $\frac { 3 x ^ { 2 } } { 4 } \div \frac { x ^ { 3 } } { 24 }$

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers. -The algebraic expression $0.07 \mathrm {~d} ^ { 3 / 2 }$ describes the duration of a storm, in hours, whose diameter is d miles. Use a calculator to determine the duration of a storm with a diameter of 13 miles. Round to The nearest hundredth.

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $- 8 a x ^ { 7 } \left( - 12 a x ^ { 5 } - 5 x ^ { 2 } + 6 a \right)$

Use the distributive property to rewrite a sum as a product or the product as a sum. --(-4 - 4r)

Factor by any method. - $128 x ^ { 4 } - 50$

Insert $\subseteq$ or $\nsubseteq$ in the blank to make the statement true. - $\{ - 11,6 , - 12,0,10 \}$ ______ $\varnothing$

Identify the set as finite or infinite. - $\left\{ 1 , \frac { 1 } { 2 } , \frac { 1 } { 4 } , \frac { 1 } { 8 } , \ldots , \right\}$

Simplify the expression. Assume all variables represent positive real numbers. - $( \sqrt { 6 } - 3 ) ( \sqrt { 7 } - 5 )$

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $z ^ { - 2 / 5 } \cdot z ^ { 3 / 5 }$

Factor the trinomial, if possible. - $50 m ^ { 2 } - 140 m n + 98 n ^ { 2 }$