Questions over hw?
Skills Check 1. x2 + 2x – 15 2. x2 + 14x + 24 3. 2x2 + 6x – 36 Factor. 1. x2 + 2x – 15 2. x2 + 14x + 24 3. 2x2 + 6x – 36 4. 3x2 + 13x + 4 5. 4x2 + 16x + 15
EOCT Practice Question of the Day
CCGPS Geometry Day 48 (10-18-13) UNIT QUESTION: How are real life scenarios represented by quadratic functions? Today’s Question: What are special products when factoring quadratics? Standard: MCC9-12.A.SSE.3a
Difference of Two Perfect Squares
Difference of Squares A binomial with a subtraction sign in between terms that are both PERFECT SQUARES
To Factor Difference of Squares One parenthesis is a plus and one is a minus. Take the square root of each term.
Example
Example
Example
Example
Example
Perfect Square Trinomials These are special too, but can be done using our usual method of factoring trinomials
Example
Example
8. Factoring Special Cases: Word Problems A square piece of cloth must be cut to make a tablecloth. The area needed is (16x2 – 24x + 9) in2. The dimensions of the cloth are of the form cx – d, where c and d are whole numbers. Find an expression for the perimeter of the cloth. Find the perimeter when x = 11 inches. Examples! Be careful. #2 - #4 are tricky. You should know by now that you math teacher loves the tricky problems! Normal… (x + 10)(x –10) Hmm, x4 and 16 are both perfect squares… so (x2 + 4)(x2 – 4)… but wait a minute! One of those factors is a perfect square. I can factor it even more. (x2 + 4)(x –2)(x+2)… but beware! Don’t go “factor crazy” and try and factor the x2 + 4. It is one of those sums of squares that don’t factor. Hmmm, again… 100 is a perfect square and so is 400, but I notice that the polynomials has a GCF of 100. I can factor that out first. 100(x2 – 4). Now I can factor x2- 4. So 100(x-2)(x+2) Not a difference of squares, but maybe I can do what I did in #3 to factor this one. The GCF is 3. I can factor this to 3(x2 – 25) = 3(x-5)(x+5) Not a polynomial, but It is a difference of squares. So (15x – 11y)(15x + 11y)
9. Factoring Special Cases: Word Problems A company produces square sheets of aluminum, each of which has an area of (9x2 + 6x + 1) m2. The side length of each sheet is in the form cx + d, where c and d are whole numbers. Find an expression in terms of x for the perimeter of a sheet. Find the perimeter when x = 3 m. Examples! Be careful. #2 - #4 are tricky. You should know by now that you math teacher loves the tricky problems! Normal… (x + 10)(x –10) Hmm, x4 and 16 are both perfect squares… so (x2 + 4)(x2 – 4)… but wait a minute! One of those factors is a perfect square. I can factor it even more. (x2 + 4)(x –2)(x+2)… but beware! Don’t go “factor crazy” and try and factor the x2 + 4. It is one of those sums of squares that don’t factor. Hmmm, again… 100 is a perfect square and so is 400, but I notice that the polynomials has a GCF of 100. I can factor that out first. 100(x2 – 4). Now I can factor x2- 4. So 100(x-2)(x+2) Not a difference of squares, but maybe I can do what I did in #3 to factor this one. The GCF is 3. I can factor this to 3(x2 – 25) = 3(x-5)(x+5) Not a polynomial, but It is a difference of squares. So (15x – 11y)(15x + 11y)
Classwork SPW 13.9
Homework Review Sheet