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Elementary Algebra
Factoring

1
The Greatest Common Factor and Factoring by Grouping

Problem  1
practice icon

Find the greatest common factor for \(3x^5+12x^2\)

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

Find the greatest common factor for \(8a^3b^2+16a^2b^3+20a^3b^3\)

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Matt cc
Matt
David espanol spanish
David
Problem  3

Find the greatest common factor for \(2x+9\).

Choose instructor to watch:
Mrs. Mooney cc
Mrs. Mooney
Nathan cc
Nathan
Breylor cc
Breylor
Stephanie cc
Stephanie
Problem  4
practice icon

Factor \(3x-15\)

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

Factor \(5x^3-15x^2\)

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Matt cc
Matt
David espanol spanish
David
Problem  6
practice icon

Find the greatest common factor for \(16x^5-20x^4+8x^3\)

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Brooke cc
Brooke
Gordon cc
Gordon
David espanol spanish
David
Problem  7

Find the greatest common factor from
\(-6x^3y-18x^2y^2+12xy^3\)

Choose instructor to watch:
Mrs. Mooney cc
Mrs. Mooney
Nathan cc
Nathan
Breylor cc
Breylor
Stephanie cc
Stephanie
Problem  8
practice icon

Find the greatest common factor for \(3a^2b-6a^3b^2+9a^3b^3\)

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Elisabeth cc
Elisabeth
Matt cc
Matt
David espanol spanish
David
Problem  9
practice icon

Factor \(ax+bx+ay+by\).

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Brooke cc
Brooke
Gordon cc
Gordon
David espanol spanish
David
Problem  10
practice icon

Factor \(2x^2+5ax-2xy-5ay\).

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Brooke cc
Brooke
Gordon cc
Gordon
David espanol spanish
David
Problem  11

Factor: \(3ax-10+15x-2a\)

Choose instructor to watch:
Mrs. Mooney cc
Mrs. Mooney
Nathan cc
Nathan
Breylor cc
Breylor
Stephanie cc
Stephanie
Mini Lecture

Mini Lecture
Factor out the greatest common factor.

  1. \(6a+9\)

  2. \(15x^3-25x^2+30x\)

Factor by grouping.

  1. \(xy+5x+3y+15\)

  2. \(ab+7a-3b-21\)

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

2
Factoring Trinomials

Problem  1
practice icon

Factor \(x^2+8x+12\).

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Gordon cc
Gordon
David espanol spanish
David
Problem  2

Factor: \(x^2-7x+12\)

Choose instructor to watch:
Mrs. Mooney cc
Mrs. Mooney
Stephanie cc
Stephanie
Breylor cc
Breylor
Nathan cc
Nathan
Problem  3
practice icon

Factor \(x^2-2x-15\).

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

Factor: \(x^2+3x-18\)

Choose instructor to watch:
Mrs. Mooney cc
Mrs. Mooney
Stephanie cc
Stephanie
Breylor cc
Breylor
Nathan cc
Nathan
Problem  5
practice icon

Factor \(x^2+8xy+12y^2\).

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Brooke cc
Brooke
David cc
David
David espanol spanish
David
Problem  6
practice icon

Factor \(2x^2+10x-28\).

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Brooke cc
Brooke
Gordon cc
Gordon
David espanol spanish
David
Problem  7
practice icon

Factor \(3x^3-3x^2-18x\).

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Brooke cc
Brooke
Matt cc
Matt
David espanol spanish
David
Problem  8

Factor: \(-y^2+11y-24\)

Choose instructor to watch:
Mrs. Mooney cc
Mrs. Mooney
Breylor cc
Breylor
Nathan cc
Nathan
Mini Lecture

Mini Lecture
Factor

  1. \(x^2+7x+12\)

  2. \(a^2+10a+21\)

  3. \(3a^2-3a-60\)

  4. \(100p^2-1300p+4000\)

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

3
More on Factoring Trinomials

Problem  1
practice icon

Factor \(6a^2+7a+2\).

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

Factor \(4x^2-x-3\).

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

Factor \(12y^3+10y^2-12y\).

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

Factor: \(6x^2-17x+12\)

Choose instructor to watch:
Mrs. Mooney cc
Mrs. Mooney
Breylor cc
Breylor
Nathan cc
Nathan
Problem  5

Factor: \(8x^2+26x-15\)

Choose instructor to watch:
Mrs. Mooney cc
Mrs. Mooney
Breylor cc
Breylor
Nathan cc
Nathan
Problem  6
practice icon

Factor \(30x^2y-5xy^2-10y^3\).

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Brooke cc
Brooke
Matt cc
Matt
Cynthia espanol spanish
Cynthia
Problem  7
practice icon

A ball is tossed into the air with an upward velocity of \(16\) feet per second from the top of a building \(32\) feet high. The equation that gives the height of the ball above the ground at any time \(t\) is \[h=32+16t-16t^2\] Factor the right side of this equation and then find \(h\) when \(t\) is \(2\).

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Stefanie cc
Stefanie
Matt cc
Matt
Cynthia espanol spanish
Cynthia
Mini Lecture

Mini Lecture
Factor.

  1. \(2x^2+7x+3\)

  2. \(4y^2-11y-3\)

  3. \(3x^2-xy-14y^2\)

  4. \(10a^3-6a^2-4a\)

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

4
Special Factoring Patterns

Problem  1
practice icon

Factor \(25x^2-60x+36\).

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

Factor \(5x^2+30x+45\).

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Gordon cc
Gordon
David espanol spanish
David
Problem  3
practice icon

Factor \(16x^2-25\).

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Cynthia espanol spanish
Cynthia
Problem  4

Factor: \(1-36a^2\)

Choose instructor to watch:
Mrs. Mooney cc
Mrs. Mooney
Breylor cc
Breylor
Nathan cc
Nathan
Problem  5

Factor: \(4x^2+16y^2\)

Choose instructor to watch:
Mrs. Mooney cc
Mrs. Mooney
Breylor cc
Breylor
Nathan cc
Nathan
Problem  6
practice icon

Factor \(x^4-y^4\).

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Mrs. Mooney cc
Mrs. Mooney
Gordon cc
Gordon
Gordon espanol spanish
Gordon
Problem  7

Factor \((x-3)^2-25\)

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
David cc
David
David espanol spanish
David
Problem  8
practice icon

Verify the formulas below.
\(a^3+b^3=(a+b)(a^2-ab+b^2)\)
\(a^3-b^3=(a-b)(a^2+ab+b^2)\)

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Betsy cc
Betsy
David cc
David
Anthony espanol spanish
Anthony
Problem  9
practice icon

Factor \(x^3-8\).

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Matt cc
Matt
Anthony cc
Anthony
Cynthia espanol spanish
Cynthia
Problem  10
practice icon

Factor \(y^3+27\).

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Matt cc
Matt
Edwin espanol spanish
Edwin
Problem  11
practice icon

Factor \(64+t^3\).

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Brooke cc
Brooke
Matt cc
Matt
Cynthia espanol spanish
Cynthia
Problem  12
practice icon

Factor \(27x^3+125y^3\).

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Brooke cc
Brooke
Matt cc
Matt
Edwin espanol spanish
Edwin
Problem  13
practice icon

Factor \(a^3-\displaystyle\frac{1}{8}\).

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Matt cc
Matt
Cynthia espanol spanish
Cynthia
Problem  14
practice icon

Factor \(x^6-y^6\).

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Mrs. Mooney cc
Mrs. Mooney
Mr. McKeague cc
Mr. McKeague
Edwin espanol spanish
Edwin
Mini Lecture
practice icon

Mini Lecture
Factor.

  1. \(x^2-9\)

  2. \(9a^2-16b^2\)

  3. \(a^2-10a+25\)

  4. \(4a^2+12a+9\)

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

5
Factoring: A General Review

Problem  1
practice icon

Factor \(2x^5-8x^3\).

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 \(3x^4-18x^3+27x^2\).

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

Factor: \(y^4+27y\)

Choose instructor to watch:
Mrs. Mooney cc
Mrs. Mooney
Breylor cc
Breylor
Nathan cc
Nathan
Problem  4
practice icon

Factor \(6a^2-11a+4\).

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

Factor \(6x^3-12x^2-48x\).

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Brooke cc
Brooke
Matt cc
Matt
Edwin espanol spanish
Edwin
Problem  6
practice icon

Factor \(2ab^5+8ab^4+2ab^3\).

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

Factor \(xy+8x+3y+24\).

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Brooke cc
Brooke
Matt cc
Matt
Edwin espanol spanish
Edwin
Problem  8

Mini Lecture
Factor:

  1. \(x^2-81\)

  2. \(y^2-10y+25\)

  3. \(xy-5x+2y-10\)

  4. \(3x^2+15xy+18y^2\)

  5. \(49x^2+9y^2\)

  6. \(6a^2-ab-15b^2\)

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

6
Solving Equations by Factoring

Problem  1

Solve: \((2x-5)(x+4)=0\)

Choose instructor to watch:
Mrs. Mooney cc
Mrs. Mooney
Breylor cc
Breylor
Nathan cc
Nathan
Problem  2
practice icon

Solve \(2x^2-5x=12\)

Choose instructor to watch:
Jesse cc
Jesse
Betsy cc
Betsy
Gordon cc
Gordon
Anthony espanol spanish
Anthony
Problem  3
practice icon

Solve \(16a^2-25=0\)

Choose instructor to watch:
Betsy cc
Betsy
Preston cc
Preston
Anthony espanol spanish
Anthony
Problem  4
practice icon

Solve \(4x^2=8x\)

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Betsy cc
Betsy
Gordon cc
Gordon
Anthony espanol spanish
Anthony
Problem  5
practice icon

Solve \(x(2x+3)=44\)

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

Solve \(5^2=x^2+(x+1)^2\)

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

Solve \(24x^3=-10x^2+6x\)

Choose instructor to watch:
Mr. McKeague cc
Mr. McKeague
Betsy cc
Betsy
Preston cc
Preston
Anthony espanol spanish
Anthony
Mini Lecture

Mini Lecture
Solve.

  1. \(x(x+1)(x-3)=0\)

  2. \(x^2-9x+20=0\)

  3. \(a^2+25=10a\)

  4. \(x^2+6x=0\)

  5. \(4y^3-2y^2-30y=0\)

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

7
Applications

Problem  1

The product of two consecutive odd integers is 63. Find the integers.

Choose instructor to watch:
Preston cc
Preston
Gordon cc
Gordon
Stefanie cc
Stefanie
Gordon espanol spanish
Gordon
Problem  2
The sum of two numbers is 13. Their product is 40. Find the numbers.
Choose instructor to watch:
Stefanie cc
Stefanie
Aaron cc
Aaron
Cynthia espanol spanish
Cynthia
Problem  3
The length of a rectangle is 3 more than twice the width. The area is 44 square inches. Find the dimensions.
Choose instructor to watch:
Stefanie cc
Stefanie
Gordon cc
Gordon
Gordon espanol spanish
Gordon
Problem  4
The numerical value of the area of a square is twice its perimeter. What is the length of its side?
Choose instructor to watch:
Aaron cc
Aaron
Stefanie cc
Stefanie
Preston cc
Preston
Cynthia espanol spanish
Cynthia
Problem  5
The three sides of a right triangle are three consecutive integers. Find the lengths of the three sides.
Choose instructor to watch:
Stefanie cc
Stefanie
Gordon cc
Gordon
Gordon espanol spanish
Gordon
Problem  6

The hypotenuse of a right triangle is \(13\) inches, and one leg is \(7\) inches longer than the other leg. Find the lengths of the two legs.

Choose instructor to watch:
Mrs. Mooney cc
Mrs. Mooney
Breylor cc
Breylor
Nathan cc
Nathan
Problem  7
practice icon

A company can manufacture \(x\) hundred items for a total cost of \(C=300+500x-100x^2\). How many items were manufactured if the total cost is \(\$900\)?

Choose instructor to watch:
Stefanie cc
Stefanie
Gordon cc
Gordon
Gordon espanol spanish
Gordon
Problem  8
practice icon

A manufacturer of portable radios knows that the number of radios she can sell per week is given by the equation \(x=1,300-100p\) where \(p\) is the price per radio. What price should she charge to have a weekly revenue of \(\$4,000\)?

Choose instructor to watch:
Aaron cc
Aaron
Stefanie cc
Stefanie
Preston cc
Preston
Cynthia espanol spanish
Cynthia
Mini Lecture

Mini Lecture

  1. The product of two consecutive even integers is \(80\). Find the two integers.

  2. One number is two more than five times another. Their product is \(24\). Find the numbers.

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