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Lecture Comments (1)

0 answers

Post by John White on March 21 at 08:25:47 PM

The last exercise should have been w as a variable instead of x.

Factoring Trinomials with Leading Coefficient of 1

  • To factor a trinomial with leading coefficient 1, find two numbers whose sum is equal to the coefficient of the linear term of the trinomial and whose product is equal to the constant term of the trinomial. Use trial and error to do this.
  • If all the terms of the trinomial are positive, then all the factors will have positive terms.
  • If the constant term is positive and the linear term is negative, the factors will have two negative constant terms.
  • If the constant term is negative, the factors will have constant terms that have opposite signs.
  • You can solve some quadratic equations by factoring the trinomial and then using the zero product property

Factoring Trinomials with Leading Coefficient of 1

Factor:
x2 + 16x + 60
  • ( x + p )( x + q )
  • p + q = b = 16
  • pq = c = 60
  • p = 6,q = 10
  • ( x + 6 )( x + 10 )
  • Foil to check your work.
  • ( x + 6 )( x + 10 )
  • x2 + 10x + 6x + 60
x2 + 16x + 60
Factor:
w2 + 11w + 24
  • p + q = b = 11
  • pq = c = 24
  • p = 3,q = 8
( w + 3 )( w + 8 )
Factor:
k2 + 8k + 16
  • p + q = b = 8
  • pq = c = 16
  • p = 4,q = 4
( k + 4 )( k + 4 )
Factor:
y2 − 7y + 12
  • ( x − p )( x − q )
  • p + q = b = − 7
  • pq = c = 12
  • p = − 3,q = − 4
( y − 3 )( y − 4 )
Factor:
g2 − 6g + 8
( g − 2 )( g − 4 )
Factor:
b2 − 11b + 18
( b − 2 )( b − 9 )
Factor:
8n − 20 + n2
  • n2 + 8n − 20
  • c〈0 .
  • ( x + p )( x − q )
( n − 2 )( n + 10 )
Factor:
r2 + 17r − 18
( r − 1 )( r + 18 )
Factor:
s2 − 36 = − 9s
  • s2 + 9s − 36 = 0
( s − 3 )( s + 12 )
Factor:
22 + 40 = 132
  • 22 − 132 + 40 = 0
( 2 − 5 )( 2 − 8 )
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 Trinomials with Leading Coefficient of 1

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 0:07
    • Leading Coefficient
    • Example
  • Rules for Signs 2:42
    • P and Q Both Positive
    • P and Q Both Negative
    • P and Q Opposite Signs
  • Solving Equations 5:18
    • Example
  • Example 1: Factor the Polynomial 7:41
  • Example 2: Factor the Polynomial 12:33
  • Example 3: Factor the Polynomial 16:39
  • Example 4: Solve the Polynomial 21:35