To factor:
into ( + one number)(+ another number), note
that
is the sum of the two numbers and
is the
product of the two numbers
So We’ll be looking for the 2 numbers whose
product is
and whose sum is
Note:
there are fewer choices for the product, so
that’s why we start there first
Factoring Trinomials

Example
Factor the polynomial
Since our two numbers must have a product of 30 and
sum of 13, the two numbers must both be positive
Note: there are other factors, but once we find a pair
that works, we do not have to continue
searching.
Factoring quadratic polynomials
Positive factors of 30
Sum of factors
1
And 30
31
2
And 15
17
3
And 10
13

Example
Factor the polynomial
Factoring quadratic polynomials

Example
Factor the polynomial
Since our two numbers must have a product of -35 and
Factoring quadratic polynomials

Example
Factor the polynomial
Since our two numbers must have a product of 10 and
Prime polynomials

You should always check your factoring
results by multiplying the factored
polynomial to verify that is equal to the
original polynomial
Many times you can detect computational
errors in the signs of your numbers by
checking your results
Check your result!

Example
Solve
•
First write the quadratic equation in
standard form
•
Now we factor the quadratic
•
We set each factor equal to 0
which will simplify to
Solving quadratic
equations

Example continued
Check both possible answers in the original
equation
true
true
So our solutions for
are
8
or
-3
Solving quadratic
equations

Solving quadratic
equations by the quadratic
formula

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- Summer '19
- Math, Calculus, Factoring, Equations, Quadratic equations, Quadratic equation, Elementary algebra, Perfect Square Trinomials