Algebra II
Unit 4 Day 4: 5-3 Factoring Quadratics to Solve
Name: _______________________
Date: ____________ Block: _____
Special Forms
A. Factoring trinomials of the form x2 + bx + c: (coefficient a = 1)
Example A: Factor x2 + 3x + 2
Example B: Factor x2 – 8x – 20
The factors are (x + 2)(x + 1) .
The factors are (x – 10)(x + 2).
CHECK: (x + 2)(x + 1) = x2 + 1x + 2x + 2 = x2 + 3x + 2
CHECK: (x – 10)(x + 2) = x2 + 2x – 10x – 20 = x2 – 8x - 20
**FOIL**
**FOIL**
Factor the following trinomials:
1. x2 + 5x + 6
2. x2 + 9x + 20
3. x2 – 10x + 21
1. _______________
CHECK:
2. _______________
CHECK:
3. _______________
CHECK:
B. Factoring binomials of the form a2 – b2 : (difference of squares)
Example C: Factor x2 – 16
The factors are (x + 4)(x – 4)
CHECK: (x + 4)(x – 4) = x2 – 4x + 4x – 16 = x2 - 16
**FOIL**
Example D: Factor 25x2 – 100
First factor the GCF: 25(x2 – 4)
Then factor the binomial: 25(x + 2)(x – 2)
CHECK: 25(x + 2)(x – 2) = 25(x2 – 2x + 2x – 4) =
25(x2 – 4) = 25x2 – 100
Factor the following binomials:
4. x2 – 25
5. x2 – 4
6. 4x2 – 36
4. _______________
CHECK:
5. _______________
CHECK:
6. _______________
CHECK:
C. Factoring trinomial squares of the form a2 + 2ab + b2 or a2 – 2ab + b2: (perfect square trinomials)
Example E: Factor x2 + 10x + 25
Example F: Factor x2 – 6x + 9
2
The factors are (x + 5)(x + 5) = (x + 5)
The factors are (x – 3)(x – 3) = (x – 3)2
2
2
CHECK: (x + 5)(x + 5) = x + 5x + 5x + 25 = x + 10x + 25
CHECK: (x – 3)(x – 3) = x2 – 3x – 3x + 9 = x2 – 6x + 9
Factor the following trinomials:
7. x2 + 14x + 49
8. x2 + 8x + 16
9. x2 - 12x + 36
7. _______________
CHECK:
8. _______________
CHECK:
9. _______________
CHECK:
D. Factoring Other Forms of Polynomials:
1. Always factor a GCF out first
2. Use the special forms formulas on first page or guess and check.
3. If after factoring out a GCF a trinomial of the form ax2 + bx + c remains, remember the O “outer” and
I “inner” product from FOIL are numbers whose product is “ac” and that add up to “b”. Find numbers that
meet that requirement and write a polynomial with 4 terms.
4. Finish factoring by grouping.
10. x2 - 7x - 15
11. 2x2 - 3x - 5
12. 4x2 + 4x - 24
10. _______________
CHECK:
11. _______________
CHECK:
12. _______________
CHECK:
13. 3x2 + 21x + 36
14. 4x3 - 144x
15. 4x2 + 4x - 15
13. _______________
CHECK:
14. _______________
CHECK:
15. _______________
CHECK:
16. 5x2 + 2x + 7
17. -12x4 + 3x2
18. 44 - 15x + x2
16. _______________
CHECK:
17. _______________
CHECK:
18. _______________
CHECK: