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 7.1-7.4 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.

Homework Text p. 375, #4-34 evens

Homework Text p. 375, #4-34 evens

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

“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.

GCF of Variable Expressions Remember this? Find the GCF of 12x²y and 6xy³. Write the prime factorization of each and then compare. 12x²y: 2 · 2 · 3 · x · x · y 6xy³: 2 · 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.

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

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

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

“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

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.

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.

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.

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.

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

Factor Challenge

Homework Text p. 381, #4-40 evens

Homework Greatest Common Factor worksheet #34 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20)