Section 4.1: Finding Roots By Factoring
February 11, 2016
4-1: Finding Roots of Polynomial Expression
Solve by factoring to find the zeros/roots.
I. Factoring a Quadratic
"FOIL" backwards
*find two binomials that multiply to get the
quadratic
Steps
1.) Break the first term into possible factors
2.) Break the last term into possible factors
3.) Find the combination that will multiple the first
factors with the last factors and then add to make
the middle term (Basically find the O and I in FOIL)
Solve by factoring.
1.
x2 - 6x - 16 = 0
3. x2 + 8x - 20 = 0
Pre­Calc
2. 3x2 + x - 2 = 0
4. 4x2 - 11x + 6 = 0
Section 4.1: Finding Roots By Factoring
II. Factor a Quartic ax4 + bx2 + c
Just like factoring a quadratic!
Use x2 instead of x in each factor
5. t4 - 5t2 - 36 = 0
6. t4 - 1 = 0
7. 9t4 - 35t2 - 4 = 0
Pre­Calc
February 11, 2016
Section 4.1: Finding Roots By Factoring
III. Factoring Cubics
2 Options:
1. ax3 + bx2 + cx = 0
*factor out an x
2. ax3 + bx2 + cx + d = 0
*factor by grouping
Examples.
8. x3 + 2x2 - 8x = 0
Factor by Grouping
1. Group the first 2 terms & the last two terms
2. Pull out the GCF of each group
ax2 (x - b) + c(x - b) = (ax2 + c)(x - b)
3. What's left in both parenthesis should be the same
4. Create two factors by distributing the parenthesis out.
Examples
9. 4x3 - 2x2 + 16x - 8 = 0
Pre­Calc
February 11, 2016
Section 4.1: Finding Roots By Factoring
Factor.
10. 2x3 + 5x2 + 6x + 15 = 0
11. 12x3 + 2x2 - 30x - 5 = 0
12. 21x3 - 84x2 + 15x - 60 = 0
13. 28x3 + 16x2 - 21x - 12= 0
Pre­Calc
February 11, 2016