Exam 5: Exponents, Polynomials, and Polynomial Functions

Perform the indicated operations. $\left( - 4 x ^ { 2 } + 7 x + 5 \right) - \left( - 6 x ^ { 2 } - 6 x + 1 \right) - \left( 6 x ^ { 2 } + 10 x + 5 \right)$

(Essay)

4.7/5

(29)

Question 201

Perform the operation. Leave answer in scientific notation. $\frac { 1.44 \times 10 ^ { - 13 } } { 1.2 \times 10 ^ { 3 } }$

(Multiple Choice)

4.8/5

(38)

Question 202

Solve the equation by first clearing it of fractions. $\frac { 5 } { 7 } a ^ { 2 } = \frac { 6 } { 7 } - a$ , a = __________ If there is more than one solution, separate your answers with commas.

(Essay)

4.9/5

(35)

Question 203

Multiply. $\left( 3 a ^ { 2 } b c ^ { 6 } \right) \left( - 6 a ^ { 3 } b ^ { 2 } c ^ { 2 } \right) \left( 6 a ^ { 4 } c ^ { 5 } \right)$

(Multiple Choice)

5.0/5

(29)

Question 204

Factor completely: $128 x ^ { 2 } - 160 x y + 50 y ^ { 2 }$

(Essay)

4.8/5

(35)

Question 205

Write the numbers in scientific notation and perform the operations. $( 910,000,000,000 ) ( 430,000,000 )$ Give the answer in scientific notation. $Write the numbers in scientific notation and perform the operations. ( 910,000,000,000 ) ( 430,000,000 ) Give the answer in scientific notation. \times 10 ^ { - } Give the answer in standard notation. $ $\times 10 ^ { - }$ Give the answer in standard notation.

(Short Answer)

4.9/5

(27)

Question 206

Which of the following expressions is a polynomial?

(Multiple Choice)

4.8/5

(33)

Question 207

Solve: $12 x ^ { 2 } + 23 x = 24$

(Multiple Choice)

4.9/5

(39)

Question 208

Subtract. $\left( x ^ { 2 } - 6 x + 6 \right) - \left( 5 x ^ { 2 } + x + 1 \right)$

(Essay)

4.9/5

(29)

Question 209

Find the product. $\left( y ^ { 3 } - 3 \right) \left( y ^ { 3 } + 3 \right)$

(Multiple Choice)

4.9/5

(41)

Question 210

Factor completely: $x ^ { 4 } - 24 x ^ { 2 } - 25$

(Multiple Choice)

4.8/5

(29)

Question 211

Write the number in scientific notation. 4200 $Write the number in scientific notation. 4200 \times 10 ^ { - }$ $\times 10 ^ { - }$

(Short Answer)

4.9/5

(30)

Question 212

Determine whether the equation is a quadratic equation. $k ^ { 3 } - 6 k ^ { 2 } + k - 15 = 0$

(Multiple Choice)

4.9/5

(33)

Question 213

Let $f ( x ) = ( x - 4 ) ( x + 4 )$ and $g ( x ) = 6 x$ . Find all values of x such that $f ( x ) = g ( x )$

(Essay)

4.9/5

(34)

Question 214

Perform the indicated operation: $( 3 a - 2 ) \left( 5 a ^ { 2 } - 3 a - 7 \right)$

(Multiple Choice)

4.9/5

(24)

Question 215

Solve the equation. $- z ^ { 4 } + 13 z ^ { 2 } - 36 = 0$ , z = __________ If there is more than one solution, separate your answers with commas.

(Essay)

4.8/5

(27)

Question 216

Write $6.38 \times 10 ^ { 5 }$ in standard notation.

(Multiple Choice)

4.7/5

(29)

Question 217

Simplify the expression. $\left( \frac { 2 } { 7 } \right) ^ { - 2 }$

(Essay)

4.8/5

(36)

Question 218

Simplify the expression. Assume that variables represent nonzero real numbers. Write the answer using positive exponents only. $\left( \frac { a ^ { 2 } } { b ^ { 3 } } \right) ^ { - 5 }$

(Multiple Choice)

4.9/5

(37)

Question 219

If $f ( x ) = - 3 x ^ { 3 } - x ^ { 2 } + 4 x - 3$ , find $f ( - 1 )$ .

(Multiple Choice)

4.8/5

(34)

Question 220

Perform the indicated operations. $\left( - 4 x ^ { 2 } + 7 x + 5 \right) - \left( - 6 x ^ { 2 } - 6 x + 1 \right) - \left( 6 x ^ { 2 } + 10 x + 5 \right)$

Perform the operation. Leave answer in scientific notation. $\frac { 1.44 \times 10 ^ { - 13 } } { 1.2 \times 10 ^ { 3 } }$

Solve the equation by first clearing it of fractions. $\frac { 5 } { 7 } a ^ { 2 } = \frac { 6 } { 7 } - a$ , a = __________ If there is more than one solution, separate your answers with commas.

Multiply. $\left( 3 a ^ { 2 } b c ^ { 6 } \right) \left( - 6 a ^ { 3 } b ^ { 2 } c ^ { 2 } \right) \left( 6 a ^ { 4 } c ^ { 5 } \right)$

Factor completely: $128 x ^ { 2 } - 160 x y + 50 y ^ { 2 }$

Which of the following expressions is a polynomial?

Solve: $12 x ^ { 2 } + 23 x = 24$

Subtract. $\left( x ^ { 2 } - 6 x + 6 \right) - \left( 5 x ^ { 2 } + x + 1 \right)$

Find the product. $\left( y ^ { 3 } - 3 \right) \left( y ^ { 3 } + 3 \right)$

Factor completely: $x ^ { 4 } - 24 x ^ { 2 } - 25$

Write the number in scientific notation. 4200 $Write the number in scientific notation. 4200 \times 10 ^ { - }$ $\times 10 ^ { - }$

Determine whether the equation is a quadratic equation. $k ^ { 3 } - 6 k ^ { 2 } + k - 15 = 0$

Let $f ( x ) = ( x - 4 ) ( x + 4 )$ and $g ( x ) = 6 x$ . Find all values of x such that $f ( x ) = g ( x )$

Perform the indicated operation: $( 3 a - 2 ) \left( 5 a ^ { 2 } - 3 a - 7 \right)$

Solve the equation. $- z ^ { 4 } + 13 z ^ { 2 } - 36 = 0$ , z = __________ If there is more than one solution, separate your answers with commas.

Write $6.38 \times 10 ^ { 5 }$ in standard notation.

Simplify the expression. $\left( \frac { 2 } { 7 } \right) ^ { - 2 }$

Simplify the expression. Assume that variables represent nonzero real numbers. Write the answer using positive exponents only. $\left( \frac { a ^ { 2 } } { b ^ { 3 } } \right) ^ { - 5 }$

If $f ( x ) = - 3 x ^ { 3 } - x ^ { 2 } + 4 x - 3$ , find $f ( - 1 )$ .

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Exam 5: Exponents, Polynomials, and Polynomial Functions

Perform the indicated operations. (−4x2+7x+5)−(−6x2−6x+1)−(6x2+10x+5)\left( - 4 x ^ { 2 } + 7 x + 5 \right) - \left( - 6 x ^ { 2 } - 6 x + 1 \right) - \left( 6 x ^ { 2 } + 10 x + 5 \right)(−4x2+7x+5)−(−6x2−6x+1)−(6x2+10x+5)

Perform the operation. Leave answer in scientific notation. 1.44×10−131.2×103\frac { 1.44 \times 10 ^ { - 13 } } { 1.2 \times 10 ^ { 3 } }1.2×1031.44×10−13​

Solve the equation by first clearing it of fractions. 57a2=67−a\frac { 5 } { 7 } a ^ { 2 } = \frac { 6 } { 7 } - a75​a2=76​−a , a = __________ If there is more than one solution, separate your answers with commas.

Multiply. (3a2bc6)(−6a3b2c2)(6a4c5)\left( 3 a ^ { 2 } b c ^ { 6 } \right) \left( - 6 a ^ { 3 } b ^ { 2 } c ^ { 2 } \right) \left( 6 a ^ { 4 } c ^ { 5 } \right)(3a2bc6)(−6a3b2c2)(6a4c5)

Factor completely: 128x2−160xy+50y2128 x ^ { 2 } - 160 x y + 50 y ^ { 2 }128x2−160xy+50y2

Write the numbers in scientific notation and perform the operations. (910,000,000,000)(430,000,000)( 910,000,000,000 ) ( 430,000,000 )(910,000,000,000)(430,000,000) Give the answer in scientific notation. ×10−\times 10 ^ { - }×10− Give the answer in standard notation. __________

Which of the following expressions is a polynomial?

Solve: 12x2+23x=2412 x ^ { 2 } + 23 x = 2412x2+23x=24

Subtract. (x2−6x+6)−(5x2+x+1)\left( x ^ { 2 } - 6 x + 6 \right) - \left( 5 x ^ { 2 } + x + 1 \right)(x2−6x+6)−(5x2+x+1)

Find the product. (y3−3)(y3+3)\left( y ^ { 3 } - 3 \right) \left( y ^ { 3 } + 3 \right)(y3−3)(y3+3)

Factor completely: x4−24x2−25x ^ { 4 } - 24 x ^ { 2 } - 25x4−24x2−25

Write the number in scientific notation. 4200 ×10−\times 10 ^ { - }×10−

Determine whether the equation is a quadratic equation. k3−6k2+k−15=0k ^ { 3 } - 6 k ^ { 2 } + k - 15 = 0k3−6k2+k−15=0

Let f(x)=(x−4)(x+4)f ( x ) = ( x - 4 ) ( x + 4 )f(x)=(x−4)(x+4) and g(x)=6xg ( x ) = 6 xg(x)=6x . Find all values of x such that f(x)=g(x)f ( x ) = g ( x )f(x)=g(x)

Perform the indicated operation: (3a−2)(5a2−3a−7)( 3 a - 2 ) \left( 5 a ^ { 2 } - 3 a - 7 \right)(3a−2)(5a2−3a−7)

Solve the equation. −z4+13z2−36=0- z ^ { 4 } + 13 z ^ { 2 } - 36 = 0−z4+13z2−36=0 , z = __________ If there is more than one solution, separate your answers with commas.

Write 6.38×1056.38 \times 10 ^ { 5 }6.38×105 in standard notation.

Simplify the expression. (27)−2\left( \frac { 2 } { 7 } \right) ^ { - 2 }(72​)−2

Simplify the expression. Assume that variables represent nonzero real numbers. Write the answer using positive exponents only. (a2b3)−5\left( \frac { a ^ { 2 } } { b ^ { 3 } } \right) ^ { - 5 }(b3a2​)−5

If f(x)=−3x3−x2+4x−3f ( x ) = - 3 x ^ { 3 } - x ^ { 2 } + 4 x - 3f(x)=−3x3−x2+4x−3 , find f(−1)f ( - 1 )f(−1) .

A Review of Basic Algebra

Graphs, Equations of Lines, and Functions

Systems of Equations

Inequalities

Rational Expression and Equations

Radical Expressions and Equations

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conic Sections; More Graphing

Miscellaneous Topics

Filters

Perform the indicated operations. $\left( - 4 x ^ { 2 } + 7 x + 5 \right) - \left( - 6 x ^ { 2 } - 6 x + 1 \right) - \left( 6 x ^ { 2 } + 10 x + 5 \right)$

Perform the operation. Leave answer in scientific notation. $\frac { 1.44 \times 10 ^ { - 13 } } { 1.2 \times 10 ^ { 3 } }$

Solve the equation by first clearing it of fractions. $\frac { 5 } { 7 } a ^ { 2 } = \frac { 6 } { 7 } - a$ , a = __________ If there is more than one solution, separate your answers with commas.

Multiply. $\left( 3 a ^ { 2 } b c ^ { 6 } \right) \left( - 6 a ^ { 3 } b ^ { 2 } c ^ { 2 } \right) \left( 6 a ^ { 4 } c ^ { 5 } \right)$

Factor completely: $128 x ^ { 2 } - 160 x y + 50 y ^ { 2 }$

Solve: $12 x ^ { 2 } + 23 x = 24$

Subtract. $\left( x ^ { 2 } - 6 x + 6 \right) - \left( 5 x ^ { 2 } + x + 1 \right)$

Find the product. $\left( y ^ { 3 } - 3 \right) \left( y ^ { 3 } + 3 \right)$

Factor completely: $x ^ { 4 } - 24 x ^ { 2 } - 25$

Write the number in scientific notation. 4200 $Write the number in scientific notation. 4200 \times 10 ^ { - }$ $\times 10 ^ { - }$

Determine whether the equation is a quadratic equation. $k ^ { 3 } - 6 k ^ { 2 } + k - 15 = 0$

Let $f ( x ) = ( x - 4 ) ( x + 4 )$ and $g ( x ) = 6 x$ . Find all values of x such that $f ( x ) = g ( x )$

Perform the indicated operation: $( 3 a - 2 ) \left( 5 a ^ { 2 } - 3 a - 7 \right)$

Solve the equation. $- z ^ { 4 } + 13 z ^ { 2 } - 36 = 0$ , z = __________ If there is more than one solution, separate your answers with commas.

Write $6.38 \times 10 ^ { 5 }$ in standard notation.

Simplify the expression. $\left( \frac { 2 } { 7 } \right) ^ { - 2 }$

Simplify the expression. Assume that variables represent nonzero real numbers. Write the answer using positive exponents only. $\left( \frac { a ^ { 2 } } { b ^ { 3 } } \right) ^ { - 5 }$

If $f ( x ) = - 3 x ^ { 3 } - x ^ { 2 } + 4 x - 3$ , find $f ( - 1 )$ .