Section 5.4 Factoring Objectives: To find the LCM and GCF of monomials To factor special products To factor quadratic polynomials To factor by grouping

Least Common Multiple (LCM) - Greatest Common Factor (GCF) -The greatest integer that is a factor of each number. When variables are present you list common variables to the lowest power. Least Common Multiple (LCM) - The least positive integer having each number as a factor. When variables are present you list any variable to the highest power.

GCF and LCM of Monomials GCF of monomials GCF of the coefficients Variables portion – common variables to their lowest power LCM of monomials LCM of the coefficients Variables portion – any variables to their highest power

GCF and LCM of Monomials Ex 7) 48u2v2 & 6uv3w

GCF and LCM of Monomials Ex 8) 8ax2 & 12a2x

GCF PST DoS SoS Quadratics Grouping greatest common factor perfect square trinomial difference of squares sum of squares Quadratics Grouping

First rule of factoring: Always pull out what they have in common first! GCF Greatest Common Factor

Example 1 Factor:

Example 2 Factor:

Perfect Square Trinomials

How to Recognize a Perfect Square Trinomial First term is a perfect square Last term is a perfect square Perfect squares are always positive Double the product of the square roots of coefficients of the first and last terms must equal the absolute value of the middle term.

Examples 3 and 4 Factor:

Differences of Squares **YOU CANNOT FACTOR A SUM OF SQUARES!!!!!!!

Examples 5 and 6 Factor:

Example 7 Factor:

Example 9 Factor:

Example 10 Factor:

Assignment Worksheet 5.4.1

Quadratic Polynomial ax2 + bx + c

There are four permutations of the signs in a quadratic. x2 - 5x + 4 Templates: + + (x + )(x + ) sum - + (x - )(x - ) sum + - (x + )(x - ) sum - - (x + )(x - ) sum

Example 1 Factor: x2 + 9x + 14 21

Example 2 Factor: x2 + 2x - 15

Example 3 Factor: x2 - 10x + 9 23

Example 4 Factor: x2 - 10x + 24 24

Example 5 Factor: x2 + 4x - 3

Example 6 Factor: 3 – 2z – z2

Example 7 Factor: 3x2 – 8x + 5

Example 8 Factor: 15t2 – 16t + 4

Example 9 Factor: 3x6 – 48x2

Factor by Grouping

Example 13 Factor: (Rearrange with common factors first)

Assignment Worksheet 5.4.2