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INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith
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Lecture Comments (7)

1 answer

Last reply by: Jacob Davidson
Fri Mar 22, 2013 4:47 PM

Post by Jacob Davidson on March 22, 2013

I am confused on the last example. I ended up with 3x(3x-4)(8x+3). I got to this by factoring -288 to 9 and -32 equaling -23. Do you just drop the 3x to solve for x={4/3, -3/8}? Droping the 3x is the only way I can get to that solution. Is this correct?

1 answer

Last reply by: Dr Carleen Eaton
Sun Aug 12, 2012 5:57 PM

Post by Sanjay Nenawati on August 10, 2012

In Example II, when you factored the equation in the beginning, wouldn't you end up with -12 instead of -4?

2 answers

Last reply by: Sanjay Nenawati
Fri Aug 10, 2012 12:22 PM

Post by austin schneit on August 8, 2012

How does one determine which factors are associated with m & n in the formula ax2 + mx + nx + c? In example II of "Factoring General Trinomials", -9 was assigned to "m" and 16 to "n". Why couldn't this be the other way around?

Thank you!

Factoring General Trinomials

  • To factor a trinomial with a leading coefficient which is not 1, use trial and error to find the binomial factors.
  • Remember that the signs of the constant terms of the factors are based on the signs of the linear and constant terms of the trinomial. Review the material in the previous section to understand these ideas.
  • Keep in mind that not every trinomial factors into two binomial factors. Trinomials that do not are called prime trinomials.
  • You can solve some quadratic equations by factoring the trinomial and then using the zero product property

Factoring General Trinomials

Factor:
3x2 − 8x + 4
  • Factors of 3x2 = x,3
  • Factors of 4 = − 1, − 4; − 4, − 1; − 2, − 2
( x − 2 )( 3x − 2 )
Factor:
6x2 − 17x + 10
  • Factors of 6x2 = x,6x; 2x,3x
  • Factors of 10 = − 1, − 10; − 10, − 1; − 2, − 5; − 5, − 2
( x − 2 )( 6x − 5 )
Factor:
4x2 − 20x + 9
  • Factors of 4x2 = x,4x; 2x,2x
  • Factors of 9 = − 1, − 9; − 9, − 1; − 3, − 3
( 2x − 1 )( 2x − 9 )
Factor:
2x4 + 6x3 − 8x2
  • 2x2( x2 + 3x − 4 )
  • Factors of x2 = x, x
  • Factors of − 4 = 1, − 4; − 1,4; − 2,2
  • ( x − 1 )( x + 4 )
2x2( x − 1 )( x + 4 )
Factor:
12x4 + 36x3 − 21x2
  • 3x2( 4x2 + 12x − 7 )
  • Factors of 4x2 = x,4x; 2x,2x
  • Factors of − 7 = − 1,7; 1, − 7
3x2( 2x − 1 )( 2x + 7 )
Factor:
25y4 + 10y3 − 80y2
  • 5y2( 5y2 + 2y − 16 )
  • Factors of 5y2 = y,5y
  • Factors of − 16 = − 1,16; − 2,8; − 4,4; 1, − 16; 2, − 8; 4, − 4
5y2( y + 2 )( 5y − 8 )
Factor:
11m2 − 19m − 6
  • Factors of 11m2 = m,11m
  • Factors of − 6 = − 1,6; − 2,3; 1, − 6; 2, − 3
( m − 2 )( 11m + 3 )
Factor:
6c2 − 11c − 7
  • Factor of 6c2 = c,6c; 2c,3c
  • Factors of − 7 = − 1,7; 1, − 7
( 2c + 1 )( 3c − 7 )
Solve:
10n2 − 16n = 16
  • 10n2 − 16n − 16 = 0
  • Factors of 10 = 1,10; 2,5
  • Factors of 16 = 1,16; 2,8; 4,4
  • ( 2n + 4 )( 5n − 4 )
  • 2n + 4 = 0
  • 2n = 4
  • n = − 2
  • 5n − 4 = 0
  • 5n = 4
  • n = [4/5]
n{ − 2,[4/5] }
Solve:
5x2 − 6x = 11
  • 5x2 − 6x − 11 = 0
  • Factors of 5x = x,5x
  • Factors of − 11 = − 1,11; 1, − 11
  • x + 1 = 0
  • x = − 1
  • 5x − 11 = 0
  • 5x = 11
  • x = [11/5]
x{ − 1,[11/5] }

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Factoring General Trinomials

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Factoring Trinomials 0:15
    • Example
  • Grouping 7:20
    • Example
  • Rules for Signs 10:51
    • Same as Leading Coefficient is 1
  • Greatest Common Factor 12:29
    • Use Whenever Possible
    • Example
  • Prime Polynomials 13:58
    • Example
  • Solving Equations 16:55
    • Example
  • Example 1: Factor the Polynomial 18:46
  • Example 2: Factor the Polynomial 25:23
  • Example 3: Factor the Polynomial 32:37
  • Example 4: Solve the Polynomial 36:18