Exam 10: Math Exercises: Sets, Intervals, Absolute Value, and Properties

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $\left( x ^ { 10 } y ^ { 5 } \right) ^ { 1 / 5 }$

(Multiple Choice)

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Question 241

Completely factor the polynomial or state that the polynomial is prime. - $x ^ { 3 } + 40 x ^ { 2 } + 400 x$

(Multiple Choice)

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Question 242

Multiply the polynomials using a special product formula. Express the answer as a single polynomial in standard form. - $( 2 x + 1 ) ^ { 2 }$

(Multiple Choice)

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Question 243

Simplify the radical expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { - 8 x ^ { 24 } y ^ { 36 } }$

(Multiple Choice)

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Question 244

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { x ^ { 2 } - 11 x + 28 } { x ^ { 2 } - 18 x + 80 } \cdot \frac { x ^ { 2 } - 13 x + 30 } { x ^ { 2 } - 18 x + 77 }$

(Multiple Choice)

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Question 245

Find the quotient and the remainder. - $8 x ^ { 3 } + 43 x ^ { 2 } - 22 x + 48$ divided by $x + 6$

(Multiple Choice)

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Question 246

Use the commutative property of multiplication to write an equivalent algebraic expression. - $4 ( x + 3 )$

(Multiple Choice)

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Question 247

Determine whether the expression is a polynomial. If it is a polynomial, give its degree. - $\frac { x ^ { 8 } + 6 } { x ^ { 7 } + 7 }$

(Multiple Choice)

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Question 248

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { x ^ { 2 } - 9 x } { x - 4 } + \frac { 20 } { x - 4 }$

(Multiple Choice)

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Question 249

Add or subtract as indicated. Express the answer as a single polynomial in standard form. - $\left( - 7 x ^ { 2 } + 2 \right) - \left( - x ^ { 3 } + 3 x ^ { 2 } + 8 \right)$

(Multiple Choice)

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Question 250

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { \frac { 3 } { x ^ { 2 } - 4 x - 21 } - \frac { 1 } { x - 7 } } { \frac { 1 } { x + 3 } + 1 }$

(Multiple Choice)

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Question 251

Completely factor the polynomial or state that the polynomial is prime. - $10 y ^ { 2 } + 45 y - 25$

(Multiple Choice)

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Question 252

Write the interval in set-builder notation and graph the set on a number line. - $[ - 1 , \infty )$ $Write the interval in set-builder notation and graph the set on a number line. - [ - 1 , \infty )$

(Multiple Choice)

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Question 253

Perform the indicated operations. Express the answer as a single polynomial in standard form. - $6 x ( 3 x - 4 )$

(Multiple Choice)

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Question 254

Given the set sketched on the number line, identify the type of interval (open, closed, half-open, open infinite, closed infinite), write the set using set-builder notation, and write the set using interval notation. -

(Multiple Choice)

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Question 255

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $36 ^ { - 3 / 2 }$

(Multiple Choice)

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Question 256

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { \frac { x } { x + 4 } + 1 } { \frac { 12 } { x ^ { 2 } - 16 } + 1 }$

(Multiple Choice)

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(29)

Question 257

Write the interval in set-builder notation and graph the set on a number line. - $\left[ - 6 , \frac { 1 } { 4 } \right]$ $Write the interval in set-builder notation and graph the set on a number line. - \left[ - 6 , \frac { 1 } { 4 } \right]$

(Multiple Choice)

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Question 258

Completely factor the polynomial or state that the polynomial is prime. - $49 x ^ { 2 } - 126 x + 81$

(Multiple Choice)

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Question 259

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 8 } { x } + \frac { 9 } { x - 4 }$

(Multiple Choice)

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(38)

Question 260

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $\left( x ^ { 10 } y ^ { 5 } \right) ^ { 1 / 5 }$

Completely factor the polynomial or state that the polynomial is prime. - $x ^ { 3 } + 40 x ^ { 2 } + 400 x$

Multiply the polynomials using a special product formula. Express the answer as a single polynomial in standard form. - $( 2 x + 1 ) ^ { 2 }$

Simplify the radical expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { - 8 x ^ { 24 } y ^ { 36 } }$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { x ^ { 2 } - 11 x + 28 } { x ^ { 2 } - 18 x + 80 } \cdot \frac { x ^ { 2 } - 13 x + 30 } { x ^ { 2 } - 18 x + 77 }$

Find the quotient and the remainder. - $8 x ^ { 3 } + 43 x ^ { 2 } - 22 x + 48$ divided by $x + 6$

Use the commutative property of multiplication to write an equivalent algebraic expression. - $4 ( x + 3 )$

Determine whether the expression is a polynomial. If it is a polynomial, give its degree. - $\frac { x ^ { 8 } + 6 } { x ^ { 7 } + 7 }$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { x ^ { 2 } - 9 x } { x - 4 } + \frac { 20 } { x - 4 }$

Add or subtract as indicated. Express the answer as a single polynomial in standard form. - $\left( - 7 x ^ { 2 } + 2 \right) - \left( - x ^ { 3 } + 3 x ^ { 2 } + 8 \right)$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { \frac { 3 } { x ^ { 2 } - 4 x - 21 } - \frac { 1 } { x - 7 } } { \frac { 1 } { x + 3 } + 1 }$

Completely factor the polynomial or state that the polynomial is prime. - $10 y ^ { 2 } + 45 y - 25$

Write the interval in set-builder notation and graph the set on a number line. - $[ - 1 , \infty )$ $Write the interval in set-builder notation and graph the set on a number line. - [ - 1 , \infty )$

Perform the indicated operations. Express the answer as a single polynomial in standard form. - $6 x ( 3 x - 4 )$

Given the set sketched on the number line, identify the type of interval (open, closed, half-open, open infinite, closed infinite), write the set using set-builder notation, and write the set using interval notation. -

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $36 ^ { - 3 / 2 }$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { \frac { x } { x + 4 } + 1 } { \frac { 12 } { x ^ { 2 } - 16 } + 1 }$

Write the interval in set-builder notation and graph the set on a number line. - $\left[ - 6 , \frac { 1 } { 4 } \right]$ $Write the interval in set-builder notation and graph the set on a number line. - \left[ - 6 , \frac { 1 } { 4 } \right]$

Completely factor the polynomial or state that the polynomial is prime. - $49 x ^ { 2 } - 126 x + 81$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 8 } { x } + \frac { 9 } { x - 4 }$

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Filters

Exam 10: Math Exercises: Sets, Intervals, Absolute Value, and Properties

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - (x10y5)1/5\left( x ^ { 10 } y ^ { 5 } \right) ^ { 1 / 5 }(x10y5)1/5

Completely factor the polynomial or state that the polynomial is prime. - x3+40x2+400xx ^ { 3 } + 40 x ^ { 2 } + 400 xx3+40x2+400x

Multiply the polynomials using a special product formula. Express the answer as a single polynomial in standard form. - (2x+1)2( 2 x + 1 ) ^ { 2 }(2x+1)2

Simplify the radical expression. Assume all variables represent positive real numbers. - −8x24y363\sqrt [ 3 ] { - 8 x ^ { 24 } y ^ { 36 } }3−8x24y36​

Find the quotient and the remainder. - 8x3+43x2−22x+488 x ^ { 3 } + 43 x ^ { 2 } - 22 x + 488x3+43x2−22x+48 divided by x+6x + 6x+6

Use the commutative property of multiplication to write an equivalent algebraic expression. - 4(x+3)4 ( x + 3 )4(x+3)

Determine whether the expression is a polynomial. If it is a polynomial, give its degree. - x8+6x7+7\frac { x ^ { 8 } + 6 } { x ^ { 7 } + 7 }x7+7x8+6​

Perform the indicated operations and simplify the result. Leave the answer in factored form. - x2−9xx−4+20x−4\frac { x ^ { 2 } - 9 x } { x - 4 } + \frac { 20 } { x - 4 }x−4x2−9x​+x−420​

Add or subtract as indicated. Express the answer as a single polynomial in standard form. - (−7x2+2)−(−x3+3x2+8)\left( - 7 x ^ { 2 } + 2 \right) - \left( - x ^ { 3 } + 3 x ^ { 2 } + 8 \right)(−7x2+2)−(−x3+3x2+8)

Perform the indicated operations and simplify the result. Leave the answer in factored form. - 3x2−4x−21−1x−71x+3+1\frac { \frac { 3 } { x ^ { 2 } - 4 x - 21 } - \frac { 1 } { x - 7 } } { \frac { 1 } { x + 3 } + 1 }x+31​+1x2−4x−213​−x−71​​

Completely factor the polynomial or state that the polynomial is prime. - 10y2+45y−2510 y ^ { 2 } + 45 y - 2510y2+45y−25

Write the interval in set-builder notation and graph the set on a number line. - [−1,∞)[ - 1 , \infty )[−1,∞)

Perform the indicated operations. Express the answer as a single polynomial in standard form. - 6x(3x−4)6 x ( 3 x - 4 )6x(3x−4)

Given the set sketched on the number line, identify the type of interval (open, closed, half-open, open infinite, closed infinite), write the set using set-builder notation, and write the set using interval notation. -

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - 36−3/236 ^ { - 3 / 2 }36−3/2

Perform the indicated operations and simplify the result. Leave the answer in factored form. - xx+4+112x2−16+1\frac { \frac { x } { x + 4 } + 1 } { \frac { 12 } { x ^ { 2 } - 16 } + 1 }x2−1612​+1x+4x​+1​

Write the interval in set-builder notation and graph the set on a number line. - [−6,14]\left[ - 6 , \frac { 1 } { 4 } \right][−6,41​]

Completely factor the polynomial or state that the polynomial is prime. - 49x2−126x+8149 x ^ { 2 } - 126 x + 8149x2−126x+81

Perform the indicated operations and simplify the result. Leave the answer in factored form. - 8x+9x−4\frac { 8 } { x } + \frac { 9 } { x - 4 }x8​+x−49​

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Filters

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $\left( x ^ { 10 } y ^ { 5 } \right) ^ { 1 / 5 }$

Completely factor the polynomial or state that the polynomial is prime. - $x ^ { 3 } + 40 x ^ { 2 } + 400 x$

Multiply the polynomials using a special product formula. Express the answer as a single polynomial in standard form. - $( 2 x + 1 ) ^ { 2 }$

Simplify the radical expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { - 8 x ^ { 24 } y ^ { 36 } }$

Find the quotient and the remainder. - $8 x ^ { 3 } + 43 x ^ { 2 } - 22 x + 48$ divided by $x + 6$

Use the commutative property of multiplication to write an equivalent algebraic expression. - $4 ( x + 3 )$

Determine whether the expression is a polynomial. If it is a polynomial, give its degree. - $\frac { x ^ { 8 } + 6 } { x ^ { 7 } + 7 }$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { x ^ { 2 } - 9 x } { x - 4 } + \frac { 20 } { x - 4 }$

Add or subtract as indicated. Express the answer as a single polynomial in standard form. - $\left( - 7 x ^ { 2 } + 2 \right) - \left( - x ^ { 3 } + 3 x ^ { 2 } + 8 \right)$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { \frac { 3 } { x ^ { 2 } - 4 x - 21 } - \frac { 1 } { x - 7 } } { \frac { 1 } { x + 3 } + 1 }$

Completely factor the polynomial or state that the polynomial is prime. - $10 y ^ { 2 } + 45 y - 25$

Write the interval in set-builder notation and graph the set on a number line. - $[ - 1 , \infty )$ $Write the interval in set-builder notation and graph the set on a number line. - [ - 1 , \infty )$

Perform the indicated operations. Express the answer as a single polynomial in standard form. - $6 x ( 3 x - 4 )$

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $36 ^ { - 3 / 2 }$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { \frac { x } { x + 4 } + 1 } { \frac { 12 } { x ^ { 2 } - 16 } + 1 }$

Write the interval in set-builder notation and graph the set on a number line. - $\left[ - 6 , \frac { 1 } { 4 } \right]$ $Write the interval in set-builder notation and graph the set on a number line. - \left[ - 6 , \frac { 1 } { 4 } \right]$

Completely factor the polynomial or state that the polynomial is prime. - $49 x ^ { 2 } - 126 x + 81$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 8 } { x } + \frac { 9 } { x - 4 }$