Download Math 161 Notes 1.2

Section 1.2 Quadratic Equations
Objectives: Solve quadratic equations by factoring, square
root method, and the quadratic formula.
Review of Factoring
 Factoring polynomials – rewriting as a product.
 With all types of factoring, always check for a greatest
common factor (GCF) first. The GCF can be a monomial, a
binomial, or used to factor by grouping.
 Polynomials that cannot be factored are said to be prime.
Special Formulas
 Difference of Two Squares: A 2  B 2   A  B  A  B 
 Difference of Two Cubes:
A 3  B 3   A  B  A 2  AB  B 2



 Sum of Two Cubes: A 3  B 3   A  B  A 2  AB  B 2

1.2 - 2
Factoring Trinomials
 Trinomials of the Form x 2  Bx  C :
Look for two numbers whose product is C and whose sum
is B.
 Trinomials of the form Ax 2  Bx  C :
1. Look for two numbers whose product is A C and
whose sum is B.
2. Rewrite the middle term as the sum of the two
factors.
3. Factor by grouping.
 Perfect Square Trinomials: A 2  2 AB  B 2   A  B 2
A 2  2 AB  B 2   A  B 2
Work #1 - 6
Quadratic Equations
A quadratic equation is one that can be written in the form
ax 2  bx  c  0 . Also called second-degree equations.
Zero-Product Property – set each factor equal to 0, then solve
the resulting equations.
1.2 - 3
Solve Quadratic Equations by Factoring:
1. Write in standard form, if necessary.
2. Factor
3. Use zero-product property.
Work #7 - 10
Solve Quadratic Equations Using the Square Root Property:
To solve equations of the form ax 2  c  0 , isolate the
squared term on one side, then take the square root of
both sides. Don’t forget, you need the positive and the
negative roots.
Work #11 – 12
Solve Quadratic Equations Using the Quadratic Formula:
If you solve the standard form of a quadratic equation,
ax 2  bx  c  0 , by completing the square, the result is
the Quadratic Formula.
 b  b 2  4ac
x
2a
Work #13 - 19