Exam 6: Rational Expression and Equations

Divide $20 x ^ { 2 } - 7 x - 1$ by $4 x + 5$ .

Divide: $\frac { 30 x ^ { 6 } y ^ { 6 } - 24 x ^ { 2 } y ^ { 2 } + 18 x y ^ { 3 } } { - 24 x ^ { 2 } y ^ { 2 } }$

Multiply, then simplify if possible. $8 x \left( \frac { x + 4 } { 4 x } \right)$

Perform the indicated operation. Simplify, if possible. $\frac { x ^ { 2 } - 3 } { x ^ { 3 } + 4 x ^ { 2 } - 3 x - 12 } \cdot \frac { 2 x ^ { 2 } y + 8 x y } { 4 x y }$

Let $P ( x ) = 4 x ^ { 3 } - 2 x ^ { 2 } + 3 x - 2$ . Evaluate $P ( - 1 )$ by substituting the given value of x into the polynomial and simplifying. Then evaluate the polynomial by using the remainder theorem and synthetic division. $P ( - 1 )$ = __________

Perform the division. $\frac { 12 x ^ { 3 } + 11 x ^ { 2 } - 11 x - 2 } { 4 x - 3 }$

Complete the unit conversion. $\frac { 432 \text { in. } { } ^ { 2 } } { 1 \text { year } } \cdot \frac { 1 \mathrm { ft } ^ { 2 } } { 144 \text { in. } ^ { 2 } } =$ _____ __________ ( ft , years , square ft , ft per year , or square ft per year )

Express the verbal model in symbols. B varies directly as the square of u .

Divide using long division: $\frac { x ^ { 3 } + x ^ { 2 } + 5 } { x ^ { 2 } + 3 x - 1 }$

According to the Sacramento Bee newspaper, the number of words an average man speaks a day is about 12,000. How many words does an average man speak in 6 years? ( Hint: 365 days = 1 year.) __________ words

A plane can fly 270 miles in the same time as it takes a car to go 120 miles. If the car travels 90 mph slower than the plane, find the speed of the plane. __________ mph

Solve the proportion. $\frac { 3 } { 4 x } = \frac { 2 x } { 24 }$

Perform the operations and simplify the result when possible. $\frac { 3 x } { 2 x - 1 } + \frac { x + 3 } { 3 x + 2 } - \frac { 9 x } { 6 x ^ { 3 } + x ^ { 2 } - 2 x }$

The equation $y = \frac { k } { x }$ defines _________ variation.

Use synthetic division to perform the division. $\frac { 7 x ^ { 2 } + 5 + 4 x ^ { 3 } } { x + 2 }$

Express the following in symbols: D varies inversely as the square of z and jointly as the cube of x and the square root of y .

Express the verbal model in symbols. y varies inversely as the cube of u .

Express the verbal model in symbols. x varies inversely as the cube of v .

Use synthetic division to perform the division. $\frac { 16 a ^ { 3 } - 4 a ^ { 2 } - 8 a + 2 } { a - \frac { 1 } { 4 } }$

Solve the problem by writing a variation model. The distance that a car can go varies directly with the number of gallons of gasoline it consumes. If a car can go 300 miles on 12 gallons of gasoline, how far can it go on a full tank of 17 gallons?