Bellwork
1.
What is the vertex of y = 3x2 - 12x + 2?
2. What is the name of the graph of a
quadratic function?
3. In which direction does the graph of this
quadratic open: y= -2(x - 3)2 + 2?
4. What are the intercepts of the graph of
y = -1/2(x -3)(x + 1)?
5. Is y = -2(x - 2)(x + 1) wider, narrower,
or the same width as y = x2?
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Section 5.2 A
Factoring Quadratics
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Types of Factoring
Greatest Common Factor
Difference of Two Squares
Trinomials with Leading Coefficient 1
Trinomials with Leading Coefficient
other than 1
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Greatest Common
Factor
Take out the greatest common factor
of a trinomial by dividing each term
by the GCF.
Examples:
1. 16x3 - 12x2 + 4x
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2. 15xy2 - 25x2y
More GCF
3.27m3p2 + 9mp - 54p2
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4. 10x - 40y
Difference of Two
Squares
2
a
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-
2
b
= (a - b)(a + b)
Factor Each.
1. 4x2 - 9 2.
9x2 - 1
3.
16x2 + 25 4.
5.
49y4 - 9z2 6. 81p2 - 25
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1 - 25y2
Trinomials with Leading
Coefficient of 1
1.
x2 - 12x - 28
2. x2 + 3x - 10
3. x2 + 12x + 35
4. y2 - 10y - 24
5. x2 - 8x + 15
6. p2 + 3p - 40
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Trinomials with Leading
Coefficient other than 1
1.
3x2 - 17x + 10
2. 4x2 - 4x - 3
3. 49x2 - 14x + 1
4. 16y2 + 8y + 1
5. 5x2 + 17x + 14
6. 3p2 + p - 10
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Trinomials with Leading
Coefficient other than 1
7.
8x2 - 29x - 12
8. 12x2 + 19x + 5
9. 4x2 - 10x + 3
10. 16y2 + 2y - 3
11. 9x2 + 12x + 4
12. 6p2 - 13p + 5
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All together: Factor
each Completely
1.
3x2 - 27
3. 5x2 - 20
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2. 4x2 + 4x - 8
4. 14x2 + 2x - 12
All together: Factor
each Completely
5.
2u2 + 8u
7. 4x4 - 64x2
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6. 10x2 + 34x + 28
8. 30x2 - 57x + 21