1. Solving Polynomials by Factoring
Solving polynomials means that there is an equal sign. Don’t add one. If there is no equal sign, the directions probably say “factor.”
Steps:
Factor completely.
Set any part of the factored form that involves the
variable equal to zero.
3. Solve. You may need to use the quadratic formula.
4. Check your answers by plugging back into
original equation.
- b ± √b2 – 4ac 2a
This only works for quadratic (x2) equations.
x =

2. Solving Polynomials by Factoring
1. 3x4 – 108 = 0
x = ± √6, x = ± √6 i
2. x4 + 6x3 = 9x2 + 54x
x = 0, – 3, + 3, – 6

3. Solving Polynomials by Factoring
3. x3 = 1,331
x = 11, x = – 11/2 (1 ± √3 i)
4. 2x5 + 24x = 14x3
x = 0, x = ± 2, x = ± √3

4. Solving Polynomials by Factoring
5. 3(x – 1)2 = 4x + 2
x = 5/3 ± √22
6. 9x2 – 12x + 85 = 0
x = 2/3 ± 9 i

5. Solving Polynomials by Factoring
7. (x + 1)2 – 3(x – 1)2 = 6
x = 2
8. 4x2 – 28x + 49 = 0
x = 7/2

6. Solving Polynomials by Factoring
9. 12x4 + 54x2 – 30 = 0
x = ± √5 i, x = ± (√2/2)
10. x5 – 9x3 + 8x2 – 72 = 0
x = – 2, 3, – 3 and x = ± √3 i

7. Solving Polynomials by Factoring
11. 4x3 – 6x4 – 12x + 18x2 = 0
x = 0, 2/3 and x = ± √3