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Intermediate Algebra
Exponents and Polynomials

1
Sums and Differences of Polynomials

Problem  1
practice icon

Identify 6x2+2x1 as a monomial, binomial, or trinomial if possible and give the degree.

Choose instructor to watch:
Betsy cc
Betsy
Aaron cc
Aaron
Cynthia espanol spanish
Cynthia
Problem  2

Identify 5x3 as a monomial, binomial, or trinomial if possible and give the degree.

Choose instructor to watch:
Molly S. cc
Molly S.
Octabio
Octabio
Cynthia espanol spanish
Cynthia
Problem  3
practice icon

Identify 7x65x3+2x4 as a monomial, binomial, or trinomial if possible and give the degree.

Choose instructor to watch:
Molly S. cc
Molly S.
Octabio
Octabio
Cynthia espanol spanish
Cynthia
Problem  4

Identify 7x4 as a monomial, binomial, or trinomial if possible and give the degree.

Choose instructor to watch:
Molly S. cc
Molly S.
Octabio
Octabio
Cynthia espanol spanish
Cynthia
Problem  5
practice icon

Identify 15 as a monomial, binomial, or trinomial if possible and give the degree.

Choose instructor to watch:
Molly S. cc
Molly S.
Octabio
Octabio
Cynthia espanol spanish
Cynthia
Problem  6
practice icon

Add 5x24x+2 and 3x2+9x6

Choose instructor to watch:
Matt cc
Matt
Brooke cc
Brooke
Anthony cc
Anthony
Edwin espanol spanish
Edwin
Problem  7
practice icon

Find the sum of 8x3+7x26x and 10x3+3x22x6

Choose instructor to watch:
Stephanie
Stephanie
Katrina cc
Katrina
Logan cc
Logan
Julieta espanol spanish
Julieta
Problem  8
practice icon

Subtract (9x23x+5)(4x2+2x3)

Choose instructor to watch:
Anthony cc
Anthony
Brooke cc
Brooke
Matt
Matt
David espanol spanish
David
Problem  9

Subtract 4x29x+1 from 3x2+5x2

Choose instructor to watch:
Katrina
Katrina
Problem  10
practice icon

Simplify 4x3[2(3x+4)]

Choose instructor to watch:
Julieta cc
Julieta
Katrina cc
Katrina
Logan cc
Logan
Julieta cc espanol spanish
Julieta
Problem  11
practice icon

Simplify (2x+3)[(3x+1)(x7)]

Choose instructor to watch:
Katrina
Katrina
Problem  12
practice icon

Find the value of 5x33x2+4x5 when x is 2

Choose instructor to watch:
Katrina cc
Katrina
Logan cc
Logan
Cynthia espanol spanish
Cynthia
Mini Lecture

Mini Lecture
Simplify.

  1. 2x23x+10x15

  2. (5x2+6x+1)(4x2+7x2)

  3. 4x5[3(x4)]

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague

2
Multiplication of Polynomials

Problem  1
practice icon

Find the product of 4x3 and 5x23x+1

Choose instructor to watch:
Julieta cc
Julieta
Katrina cc
Katrina
Aaron cc
Aaron
Julieta cc espanol spanish
Julieta
Problem  2
practice icon

Multiply 2x3 and x+5

Choose instructor to watch:
Katrina cc
Katrina
Aaron cc
Aaron
Edwin espanol spanish
Edwin
Problem  3
practice icon

Multiply (2x3y) and (3x2xy+4y2) vertically.

Choose instructor to watch:
Katrina cc
Katrina
Aaron cc
Aaron
Cynthia espanol spanish
Cynthia
Problem  4
practice icon

Multiply: (4a5b)(3a+2b)

Choose instructor to watch:
Katrina cc
Katrina
Aaron cc
Aaron
Edwin espanol spanish
Edwin
Problem  5
practice icon

Multiply: (32t)(4+7t)

Choose instructor to watch:
Katrina cc
Katrina
Aaron cc
Aaron
Julieta cc espanol spanish
Julieta
Problem  6
practice icon

Multiply (2x+12)(4x12)

Choose instructor to watch:
Katrina cc
Katrina
Aaron cc
Aaron
Edwin espanol spanish
Edwin
Problem  7
practice icon

Multiply (a5+3)(a57)

Choose instructor to watch:
Julieta cc
Julieta
Katrina cc
Katrina
Aaron cc
Aaron
Julieta cc espanol spanish
Julieta
Problem  8
practice icon

Multiply: (2x+3)(5y4)

Choose instructor to watch:
Katrina cc
Katrina
Aaron cc
Aaron
Edwin espanol spanish
Edwin
Problem  9
practice icon

Find (4x6)2

Choose instructor to watch:
Julieta cc
Julieta
Betsy cc
Betsy
Logan cc
Logan
Julieta cc espanol spanish
Julieta
Problem  10
practice icon

Expand (x+7)2

Choose instructor to watch:
Betsy cc
Betsy
Logan cc
Logan
Edwin espanol spanish
Edwin
Problem  11
practice icon

Expand (3t5)2

Choose instructor to watch:
Julieta cc
Julieta
Betsy cc
Betsy
Logan cc
Logan
Julieta cc espanol spanish
Julieta
Problem  12
practice icon

Expand (4x+2y)2

Choose instructor to watch:
Betsy cc
Betsy
Logan cc
Logan
Edwin espanol spanish
Edwin
Problem  13
practice icon

Expand (5a3)2

Choose instructor to watch:
Julieta cc
Julieta
Betsy cc
Betsy
Logan cc
Logan
Julieta cc espanol spanish
Julieta
Problem  14
practice icon

Multiply (3x5) and (3x+5)

Choose instructor to watch:
Nathan cc
Nathan
Betsy cc
Betsy
Logan cc
Logan
Edwin espanol spanish
Edwin
Problem  15
practice icon

Multiply: (x5)(x+5)

Choose instructor to watch:
Betsy cc
Betsy
Logan cc
Logan
Julieta espanol spanish
Julieta
Problem  16
practice icon

Multiply: (2a3)(2a+3)

Choose instructor to watch:
Betsy cc
Betsy
Logan cc
Logan
Edwin espanol spanish
Edwin
Problem  17
practice icon

Multiply (x2+4)(x24)

Choose instructor to watch:
Betsy cc
Betsy
Logan cc
Logan
Julieta espanol spanish
Julieta
Problem  18
practice icon

Multiply (x32a)(x3+2a)

Choose instructor to watch:
Betsy cc
Betsy
Logan cc
Logan
Edwin espanol spanish
Edwin
Problem  19
practice icon

A company manufactures and sells prerecorded DVDs. They find that they can sell x DVDs each day at p dollars per DVD, according to the equation x=23020p. Find R(x) and R(p).

Choose instructor to watch:
Betsy
Betsy
Edwin espanol spanish
Edwin
Problem  20
practice icon

Suppose the daily cost function for the DVDs in the previous example is C(x)=200+2x. Find the profit function P(x) and then find P(130).

Choose instructor to watch:
Betsy
Betsy
Mini Lecture

Mini Lecture
Multiply.

  1. 4a3(3a2a+1)

  2. (2a3)(3a25a+1)

  3. (2a+3)(3a+2)

  4. (x2)3

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague

3
Greatest Common Factor and Factoring by Grouping

Problem  1
practice icon

Factor 8a38a248a

Choose instructor to watch:
Betsy
Betsy
Aaron
Aaron
Edwin espanol spanish
Edwin
Problem  2
practice icon

Factor 16a5b424a2b58a3b3

Choose instructor to watch:
Betsy
Betsy
Aaron
Aaron
Problem  3
practice icon

Factor 5x2(a+b)6x(a+b)7(a+b)

Choose instructor to watch:
Betsy
Betsy
Aaron
Aaron
Edwin espanol spanish
Edwin
Problem  4
practice icon

Factor a2b2+b2+8a2+8

Choose instructor to watch:
Betsy
Betsy
Aaron
Aaron
Edwin espanol spanish
Edwin
Problem  5
practice icon

Factor 155y43x3+x3y4

Choose instructor to watch:
Betsy
Betsy
Aaron
Aaron
Problem  6
practice icon

Factor x3+2x2+9x+18

Choose instructor to watch:
Betsy
Betsy
Aaron
Aaron
Mini Lecture

Mini Lecture
Factor.

  1. 3a221a+30

  2. 10x4y2+20x3y330x2y4

Factor by grouping.

  1. 3xy+3y+2ax+2a

  2. x3+2x225x50

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague

4
Factoring Trinomials

Problem  1
practice icon

Factor x2+2x15

Choose instructor to watch:
Stephanie cc
Stephanie
Betsy
Betsy
Aaron
Aaron
Julieta espanol spanish
Julieta
Problem  2
practice icon

Factor x2xy12y2

Choose instructor to watch:
Betsy
Betsy
Aaron
Aaron
Julieta espanol spanish
Julieta
Problem  3
practice icon

Factor x28x+6

Choose instructor to watch:
Betsy
Betsy
Aaron
Aaron
Julieta espanol spanish
Julieta
Problem  4
practice icon

Factor 3x415x3y18x2y2

Choose instructor to watch:
Betsy
Betsy
Aaron
Aaron
Problem  5
practice icon

Factor 2x2+13xy+15y2

Choose instructor to watch:
Betsy
Betsy
Aaron
Aaron
Julieta espanol spanish
Julieta
Problem  6
practice icon

Factor 12x4+17x2+6

Choose instructor to watch:
Molly M. cc
Molly M.
Julieta espanol spanish
Julieta
Problem  7
practice icon

Factor 2x2(x3)5x(x3)3(x3)

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Stephanie cc
Stephanie
Molly M. cc
Molly M.
Anthony espanol spanish
Anthony
Problem  8
practice icon

Factor: 3x210x8

Choose instructor to watch:
Molly M. cc
Molly M.
Julieta cc espanol spanish
Julieta
Problem  9
practice icon

Factor: 9x2+15x+4

Choose instructor to watch:
Molly M. cc
Molly M.
Julieta cc espanol spanish
Julieta
Problem  10
practice icon

Factor: 8x22x15

Choose instructor to watch:
Molly M. cc
Molly M.
Julieta cc espanol spanish
Julieta
Mini Lecture

Mini Lecture
Factor.

  1. x2+7x+12

  2. x2x12

  3. 2a5+4a4b+4a3b2

  4. 10x2+3xa18a2

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague

5
Factoring Special Products

Problem  1
practice icon

Factor x26x+9

Choose instructor to watch:
Betsy
Betsy
Aaron
Aaron
Julieta espanol spanish
Julieta
Problem  2
practice icon

Factor 16a2+40ab+25b2

Choose instructor to watch:
Betsy
Betsy
Aaron
Aaron
Julieta espanol spanish
Julieta
Problem  3
practice icon

Factor 4914t+t2

Choose instructor to watch:
Betsy
Betsy
Aaron
Aaron
Julieta espanol spanish
Julieta
Problem  4
practice icon

Factor 9x412x2+4

Choose instructor to watch:
Betsy
Betsy
Aaron
Aaron
Julieta espanol spanish
Julieta
Problem  5
practice icon

Factor (y+3)2+10(y+3)+25

Choose instructor to watch:
Betsy
Betsy
Aaron
Aaron
Julieta espanol spanish
Julieta
Problem  6
practice icon

Factor 8x224xy+18y2

Choose instructor to watch:
Betsy
Betsy
Aaron
Aaron
Julieta espanol spanish
Julieta
Problem  7
practice icon

Factor x225

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Katrina
Katrina
Aaron
Aaron
Julieta espanol spanish
Julieta
Problem  8
practice icon

Factor 49t2

Choose instructor to watch:
Katrina
Katrina
Julieta espanol spanish
Julieta
Problem  9
practice icon

Factor 81a225b2

Choose instructor to watch:
Katrina
Katrina
Julieta espanol spanish
Julieta
Problem  10
practice icon

Factor 4x61

Choose instructor to watch:
Katrina
Katrina
Julieta espanol spanish
Julieta
Problem  11
practice icon

Factor x249

Choose instructor to watch:
Katrina
Katrina
Julieta espanol spanish
Julieta
Problem  12
practice icon

Factor 16x481y4

Choose instructor to watch:
Stephanie cc
Stephanie
Julieta espanol spanish
Julieta
Problem  13
practice icon

Factor (x3)225

Choose instructor to watch:
Betsy
Betsy
Julieta espanol spanish
Julieta
Problem  14
practice icon

Factor x210x+25y2

Choose instructor to watch:
Betsy
Betsy
Julieta espanol spanish
Julieta
Problem  15
practice icon

Factor x3+2x29x18

Choose instructor to watch:
Betsy
Betsy
Julieta espanol spanish
Julieta
Problem  16

Verify the formulas a3+b3=(a+b)(a2ab+b2) and a3b3=(ab)(a2+ab+b2)

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Betsy cc
Betsy
David cc
David
Anthony espanol spanish
Anthony
Problem  17
practice icon

Factor 64+t3

Choose instructor to watch:
Betsy
Betsy
Julieta espanol spanish
Julieta
Problem  18
practice icon

Factor 27x3+125y3

Choose instructor to watch:
Betsy
Betsy
Julieta espanol spanish
Julieta
Problem  19
practice icon

Factor a318

Choose instructor to watch:
Betsy
Betsy
Julieta espanol spanish
Julieta

6
Factoring: A General Review

Problem  1
practice icon

Factor 2x58x3.

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Betsy cc
Betsy
Mrs. Mooney cc
Mrs. Mooney
David espanol spanish
David
Problem  2
practice icon

Factor 3x418x3+27x2.

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Matt cc
Matt
Anthony cc
Anthony
Cynthia espanol spanish
Cynthia
Problem  3
practice icon

Factor y3+25y.

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Matt
Matt
David cc
David
David espanol spanish
David
Problem  4
practice icon

Factor 6a211a+4.

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Stephanie cc
Stephanie
Matt cc
Matt
Cynthia espanol spanish
Cynthia
Problem  5
practice icon

Factor 2x4+16x

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Betsy cc
Betsy
Aaron cc
Aaron
Julieta espanol spanish
Julieta
Problem  6
practice icon

Factor 2ab5+8ab4+2ab3.

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Stefanie cc
Stefanie
Anthony cc
Anthony
Edwin espanol spanish
Edwin
Problem  7
practice icon

Factor 4x26x+2ax3a

Choose instructor to watch:
Stephanie cc
Stephanie
Betsy cc
Betsy
Aaron cc
Aaron
Julieta espanol spanish
Julieta
Problem  8
practice icon

Factor x6y6

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Betsy
Betsy
Preston cc
Preston
Edwin espanol spanish
Edwin

7
Solving Equations by Factoring

Problem  1
practice icon

Solve: x22x24=0

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Matt cc
Matt
David espanol spanish
David
Problem  2
practice icon

Solve 13x3=56x2+12x

Choose instructor to watch:
Betsy
Betsy
Problem  3
practice icon

Solve: 100x2=300x

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Matt cc
Matt
David espanol spanish
David
Problem  4
practice icon

Solve: (x2)(x+1)=4

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Matt cc
Matt
David espanol spanish
David
Problem  5
practice icon

Folve for x: x3+2x29x18=0

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Matt cc
Matt
Problem  6
practice icon

Solve (x+2)(3x1)=(x+2)(x+6)

Choose instructor to watch:
Molly S. cc
Molly S.
Octabio
Octabio
Cynthia espanol spanish
Cynthia
Problem  7
practice icon

The sum of the squares of two consecutive integers is 25. Find the two integers.

Choose instructor to watch:
Betsy
Betsy
Problem  8
practice icon

The lengths of the three sides of a right triangle are given by three consecutive integers. Find the lengths of the three sides.

Choose instructor to watch:
Betsy cc
Betsy
Problem  9

A rectangular garden measures 40 meters by 30 meters. A lawn of uniform width surrounds the garden and has an area of 456 square meters. Find the width of the lawn that surrounds the garden.

Choose instructor to watch:
Stephanie cc
Stephanie
Octabio
Octabio
Cynthia espanol spanish
Cynthia
Problem  10
practice icon

If an object is projected into the air with an initial velocity of v feet/second, its height h, in feet, above the ground after t seconds will be given by h=vt16t2. Find t if v=64 feet/second and h=48 feet.

Choose instructor to watch:
Betsy
Betsy
Mini Lecture

Mini Lecture.
Solve.

  1. x35x2+6x=0

  2. 110t252=0

  3. 9a3=16a

  4. (x+6)(x2)=7

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague