CCGPS Geometry
Unit 2 – Factoring Quadratics
Lesson 2.1 – Notes
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Factoring Polynomials
Introduction to Factoring out GCF
«“Factor” simply means to UNDISTRIBUTE.«
Distributed Version
Factored Version
5x(x + 3)
2x2(x – 4)
2x2 – 4x
15x2 – 5x + 30
More formal Definition:
¥ Factoring: Writing the polynomial as a product.
Steps to Factoring Out a GCF:
ê Find the GCF of all its terms (number and/or variables). For variables ALL the
terms must have the variable. Choose the smallest exponent!
ê The GCF goes to the LEFT!
ê Write the polynomial as a product by dividing the original terms of the polynomial
by the GCF.
ê The remaining factors in each term will form a polynomial. You’ll always have the
same number of terms you started with.
Examples as a class:
¥ 4 x + 6y
¥ 6x3 − 9x2 + 12 x
8
5
2
¥ y − y + y
CCGPS Geometry
Unit 2 – Factoring Quadratics
Lesson 2.1 – Notes
PRACTICE: Factor each polynomial using a GCF.
1. 10 x + 45
2.
28 x − 63
3. 18a + 42
4.
8 x + 24
5. 18 x2 − 15x + 39
6.
27a2 + 81
7. 72a8 + 33a5 − 42a3
8. 15x7 + 30 x6 − 45x3
Factoring Trinomials – Last Term POSITIVE!
ax2 + bx + c
Factoring Trinomials:
ê
ê
ê
ê
Check for GCF 1st. Divide out the GCF of each term if one exists.
When factoring ax2 + bx + c, first find factors of a and c.
Check the products of the inner and outer terms to see if the sum is b.
Signs inside both parentheses will be the SAME as the middle term!
Examples as a Class: Factor each trinomial completely.
ê 2x 2 − 15x + 18
ê 6m2 + 7m + 2
ê 20r 2 − 104r + 96