1. Do Now 2/7/19 Take out your HW from last night.
Text p. 375, #4-34 evens
Copy HW in your planner.
Text p. 381, #4-40 evens
Quiz sections Tuesday
In your notebook, define greatest common factor in your own words. Support your definition with two different examples. Include variables in one of your examples.

2. Homework Text p. 375, #4-34 evens

3. Homework Text p. 375, #4-34 evens

4. Learning Goal Learning Target
SWBAT simplify, factor, and solve polynomial expressions and equations
Learning Target
SWBAT solve polynomial equations using greatest common factors

5. “Greatest Common Factor”
Remember this?
Greatest Common Factor
The common factor of two numbers.
LARGEST
Find the GCF of 8 and 12.
List the factors of the two numbers and then compare.
8: 1, 2, 4, 8
12: 1, 2, 3, 4, 6, 12
From the list you can see that 1, 2, and 4 are common factors.
Of these 4 is the greatest common factor.

6. GCF of Variable Expressions
Remember this?
Find the GCF of 12x²y and 6xy³.
Write the prime factorization of each and then compare.
12x²y: · 2 · 3 · x · x · y
6xy³: · 3 · x · y · y · y
From the list you can see that 2, 3, x, and y are common prime
factors. The greatest common factor of is the
product of 2 · 3 · x · y, which is 6xy.

7. Section 7.4 “Solving Polynomial Equations in Factored Form”
Zero-Product Property
If ab = 0, then a = 0 or b = 0.
The zero-product property is used to solve an equation when one side of the equation is ZERO and the other side is the product of polynomial factors.
(x – 4)(x + 2) = 0
The solutions of such
an equation are called
ROOTS.
x + 2 = 0
x – 4 = 0
x = -2
x = 4

8. Solve the equations
(x – 5)(x + 1) = 0
x + 1 = 0
x – 5 = 0
x = -1
x = 5
(2x – 3)(4x + 1) = 0
4x + 1 = 0
2x – 3 = 0
x = -1/4
x = 3/2

9. Solve the equation
2x(x – 4)(x + 10) = 0
x + 10 = 0
x – 4 = 0
2x = 0
x = -10
x = 4
x = 0

10. “Solving Equations By Factoring”
2x² + 8x = 0
When using the zero-product property, sometimes you may need to factor the polynomial, or write it as a product of other polynomials. Look for the greatest common factor (GCF) of the polynomial’s terms.
GCF-
the monomial that divides evenly into EACH term of the polynomial.
Look for common terms
GCF

11. Solve Equations By Factoring
2x² + 8x = 0
Factor left side of equation
2x(x + 4) = 0
Zero product property
x + 4 = 0
2x = 0
x = -4
x = 0
The solutions of the equation are 0 and -4.

12. Solve Equations By Factoring
6x² - 15x = 0
Factor left side of equation
3x(2x - 5) = 0
Zero product property
2x - 5 = 0
3x = 0
x = 5/2
x = 0
The solutions of the equation are 0 and 5/2.

13. Solve Equations By Factoring
42p² = -14p
Bring all variables to one side
42p² + 14p = 0
Factor left side of equation
14p(3p + 1) = 0
Zero product property
3p + 1 = 0
14p = 0
p = -1/3
p = 0
The solutions of the equation are 0 and -1/3.

14. You can model the arch of a fireplace using the equation
y = -1/9(x + 18)(x – 18), where x and y are measured in inches. The x-axis represents the floor. Find the width of the arch at the floor level.

15. You can model the arch of an entrance to a train tunnel by using the equation
y = -5/16(x + 8)(x – 8),
where x and y are measured in feet. The x-axis represents the ground.
Find the width of the entrance at the ground level.
16 feet
Find the maximum height of the entrance of the train tunnel.
20 feet

16. Factor Challenge

17. Homework
Text p. 381, #4-40 evens

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