March 25-26, 2014

 The student will find the GCF of numbers and terms.  The student will use basic addition and multiplication to identify the factors of a number.  The student will demonstrate how multiplying polynomials relates to factoring polynomials.  The student will factor trinomials with one and two variables when the “a” value is 1.

 CCSS.Math.Content.A-SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x 4 – y 4 as (x 2 ) 2 – (y 2 ) 2, thus recognizing it as a difference of squares that can be factored as (x 2 – y 2 )(x 2 + y 2 ).  CCSS.Math.Content.A-SSE.3a Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.  CCSS.Math.Content.A-APR.4 Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x 2 + y 2 ) 2 = (x 2 – y 2 ) 2 + (2xy) 2 can be used to generate Pythagorean triples.  CCSS.Math.Content.F-IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

 Polynomial with three terms.

 GCF: largest quantity that is a factor of all the integers or polynomials involved.  Factors: either numbers or polynomials.  Factoring: writing a polynomial as a product of polynomials.  Prime Factors: A factor that is a prime number. One of the prime numbers that, when multiplied, give the original number.

12 and 87 and 20

6, 8 and 46 10, 25, and 100

x 3 and x 7 x 3 = x · x · x x 7 = x · x · x · x · x · x · x So the GCF is x · x · x = x 3 6x 5 and 4x 3 6x 5 = 2 · 3 · x · x · x · x · x 4x 3 = 2 · 2 · x · x · x So the GCF is 2 · x · x · x = 2x 3

a 3 b 2, a 2 b 5 and a 4 b 7 a2b2a2b2 Notice that the GCF of terms containing variables will use the smallest exponent found amongst the individual terms for each variable.

1. Find the GCF of all the terms. 2. Write the polynomial as a product by factoring out the GCF from all of the terms. 3. Remaining factors, in each term, will form a polynomial.

When a = 1, we are looking for 2 numbers whose sum is “b” and product is “c”

 The area of a rectangle is given by the trinomial x 2 - 2x What are the possible dimensions of the rectangle? Use factoring. x 2 -2x-35

10

Distribute answer out and you should get the same answer.