Math 10C
Polynomials: Lesson #7
Factoring Trinomials
Objective: By the end of this lesson, you will be able to:
- Factor trinomials symbolically
Over the past few classes, we have seen the following patterns in the terms in the factoring grid:

Middle is the ____________________ of the polynomial

Bottom right is the ____________________ of the polynomial

Other two add up to the __________________________ of
polynomial
2 x2  7 x  3
2x 2
-x
- 6x
3

Diagonal cross-products are ________________

Find the _________ of each row and column: If the top term in a column or the left term
in a row is negative, factor out a _______________ common factor.
That means in order to set up a polynomial in the grid to factor, we have to find to terms that
have the same:
 ________________ as the first and last term

___________ as the middle term
e.g. 1) Factor 3n 2  14n  15 .
Product:
Sum:
Factors:
*Make sure you actually write the factors as a product for your answer!
PSF Tips:
1. If the last term (P) is positive, the factors (F) are either:
How can you tell?
Math 10C
Polynomials: Lesson #7
2. If the last term (P) is negative, the factors (F) are:
If the middle term (S) is positive, the _____________factor will be positive.
If the middle term (S) is negative, the _____________ factor will be negative.
e.g. 2) Factor the following trinomials:
a) 6n2  17n  10
c)
b) a 2  10ab  25b2
y 2  2 y  48
Notice: There is a shortcut if the leading coefficient of the trinomial is 1:
e.g. 3) Factor x2  13x  42 using the shortcut.
Math 10C
Polynomials: Lesson #7
Sometimes you can factor out a _________ first. You should ALWAYS check for this first – if
you don’t you will almost certainly get the wrong factors from the grid!
The GCF can be a number, a variable, or both. If the first term is negative, ALWAYS factor out
the negative.
e.g. 4) Factor the following polynomials fully:
a) 15k 2  5k  10
b)  2mn2  14mn  20m
e.g. 5) The volume of the rectangular prism shown is 5n 3  40n 2  80n .
a) Find the dimensions.
b) If the height of the prism is 35 cm, and the length and width are both 11 cm, find n.
Assignment:
Factoring Polynomials Worksheet #1-9