Download Introduction to Factoring

MAT 0024
SECTION 5.1
INTRODUCTION TO FACTORING
Remember the distributive property: a(b+c) = ab + ac
Example: 4x(2x + 3) = 8x2 + 12x
To factor a polynomial is to write it as a product. In factoring we always first check for the
greatest common factor in each term and use the distributive property to rewrite the polynomial
as a product. We can check our answer by multiplying.
Factor out the greatest common factor. Check by multiplying.
1. 6x + 18
2. 20x2 – 10x
3. 8x5 – 3x4 + 4x3
4. x5y2 – x3y2 + x4y5 + x2y2
5. x(y + 3) + 4(y + 3)
6. w(x – 2) – (x – 2)
8. 3x2 – 3x –2x + 2
9. x2 – 2x – x + 2
1. 8x2 – 10x + 4
2. 8x5 + 5x4 – 3x3
3. 3x4 – 6x3 + 3x2
4. x5y5 – x4y3 + x3y3 – x3y2
5. 4x(x-9) – 3(x-9)
6. x(x+7) + (x +7)
7. 10x2 – 25x + 4x – 10
8. y3 + 8y2 – 2y – 16
9. 20x3 – 4x2 – 5x + 1
Factor by grouping:
7. x2 + 4x + 3x + 12
Practice Problems:
Homework: Page 281: odds 7-21, odds 25-41, 45, 47, 51
(033)
FACTORING THE DIFFERENCE OF TWO SQUARES
Reviewing Foil: Use foil to multiply.
1. (x + 5)(x-5)
2. (y +4)(y-4)
3. (w +3)(w-3)
4. (3x-1)(3x+1)
5. (6m +5)(6m-5)
6. (m+7)(m –7)
7. (w + 8) (w - 8)
8. (m - 10)(m + 10)
9. (4t+5)(4t-5)
Factor the following:
Examples: y2 –16 = (y +4)(y-4)
x2 – 9 = (x +3)(x-3)
x2 – y2 = (x+y)(x-y)
Check by using FOIL: Ex: (y +4)(y-4) = y2 –4y +4y – 16 = y2 – 16
Factor and check.
1. x2 – 49
2. x2 – 36
3. x2 – 25
4. x2 - 64
5. x2 – 1
6. x2 – 100
7. x2 – 16
8. y2 – 81
9. t2 – g2
10. 9x2 – 25
11. 4y2 – 49
12. 25m2 – 36
13. w2 + 9
14. m2 + 16
15. t2 – 64
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