Adding polynomials Simplify each sum Find the sum

Adding polynomials Simplify each sum. Find the sum of ______ and ______ is Procedure: 1) Make the chart 2) Add like terms 4. (-11 x 4 y + 8 xy) + (-2 xy + 7 x 4 y 4 + 9 x 3 y) + (11 xy – 6 x 4 y)

Adding Polynomials 4. (-11 x 4 y + 8 xy) + (-2 xy + 7 x 4 y 4 + 9 x 3 y) + (11 xy – 6 x 4 y)

Subtracting polynomials Simplify each difference. When _____ is subtracted from ____, the result is Which expression is equivalent to ______? Procedure: 1) Keep Change 2) Make chart 3) Add like terms 9. (-8 x + 8 x 3 – 11) – (2 x 3 – 11 – 12 x)

Subtracting polynomials (-8 x + 8 x 3 – 11) – (2 x 3 – 11 – 12 x)

Multiply monomial and binomialdistribute Procedure: 1) Multiply the outside term by the first term in the parentheses. 2) Multiply the outside term by the second term in the parentheses. 12. 4 b(3 b – 5)

Multiply monomial and binomialdistribute 12. 4 b(3 b – 5)

Multiply binomial by binomial Multiply. Simplify. What is the product of _______ and _____? A rectangle has a length of _____ and a width of _____. What is the area of the rectangle? Procedure: 1) FOIL or box method or double distribute 2) Combine like terms. 15. (-7 p – 6)(-2 p – 4)

Multiply binomial by binomial 15. (-7 p – 6)(-2 p – 4)

GCF factoring Factor the common factor out of each expression. Factor each completely. Factor completely. The expression _____ is equivalent to When _____ is factored completely, the result is What are the factors of _____? Procedure: 1) Find GCF of numbers and variables 2) Pull out GCF. (Have GCF in front and divide each term by GCF) 2 n 3 m + 2 n 3 +nm 2

GCF factoring 2 n 3 m + 2 n 3 +nm 2

Factor Trinomials with no GCF Factor each completely. Factor completely. The expression _____ is equivalent to When _____ is factored completely, the result is What are the factors of _____? Procedure: 1) BIG X 2) Double bubble (double parentheses)

Factor Trinomials with no GCF x 2 – 9 x + 18

Perfect square binomial (DOTS) with no GCF Factor each completely. Factor completely. The expression _____ is equivalent to When _____ is factored completely, the result is What are the factors of _____? Procedure: 1) Make double bubble 2) Find square root of both terms a 2 – 4

Perfect square binomial (DOTS) with no GCF Factor each completely. 27. a 2 – 4

Factor completely –with a GCF Factor each completely. Factor completely. The expression _____ is equivalent to When _____ is factored completely, the result is What are the factors of _____? Procedure: 1) Find GCF 2) Bring down GCF and divide each term by GCF 3) Factor Note: Don’t forget to bring down GCF! 2 r 2 – 10 r - 12

Factor completely – with a GCF 25. 2 r 2 – 10 r - 12

Divide trinomial by monomial •

Divide trinomial by monomial •

Scientific notation - Multiplication Simplify. Write each answer in scientific notation. The expresssion ______ is equivalent to State the value of the expression in scientific notation What is the product of _____ and ____ expressed in scientific notation? Procedure: 1) Multiply numbers 2) Add exponents 3) If necessary, “fix number” to be in scientific notation 1) Move the decimal point to the left, add 1 to exponent 2) Move decimal point to the right, bring exponent down 1 (9. 24 x 10 -3)(5. 13 x 102)

Scientific notation - Multiplication 38. (9. 24 x 10 -3)(5. 13 x 102)

Scientific notation - divide •

Scientific notation - divide •

Quadratics – finding the vertex (turning point) What is the vertex of the parabola represented by the equation ________? What is the turning point of the parabola represented by the equation ________? Procedure: 1) Find axis of symmetry by using formula x = 2) Substitute the x value you found into the equation 3) Solve for y. 4) Write vertex (x value, y value) 68. y = 2 x 2 + 4 x + 3

Quadratics – vertex (turning point) 68. y = 2 x 2 + 4 x + 3

Graphing quadratic equations Sketch the graph of each function. Graph the equation ______. Using the graph determine and state the roots of the equation _______. Procedure: 1. Find vertex 2. Use your calculator to get table of values a) Press y = and input equation b) Press 2 nd graph. c) Locate vertex by going up or down 3. Use 3 points below and above vertex from your table. 4. Graph the points 5. Connect the dots; make sure it is a smooth curve

Graphing quadratic equations 45. y = x 2

Quadratics- Finding the roots by factoring Solve each equation by factoring. The solutions of ______ are The roots of the equation _______ are What are the roots of the equation ______? Find the roots of the equation ______ algebraically. Procedure: 1. Ensure quadratic equation equals zero. 2. Factor 3. T-chart 4. Solve for x. 50. v 2 – 5 v – 9 = -3

Quadratics- Finding the roots by factoring Solve each equation by factoring. 50. v 2 – 5 v – 9 = -3

One step equations Solve each equation. Solve algebraically for x. What is the value of x in the equation _______? Procedure: Do the OPPOSITE operation to BOTH sides of the equal sign to solve the problem. This gets the variable by itself!

One-step equation •

Two-step equations •

Two-step equations •

Multi-step equations Solve each equation. Solve algebraically for x. What is the value of x in the equation _______? Procedure: 1) Distribute 2) Combine like terms 3) Do the opposite for addition/subtraction 4) Do the opposite for multiplication/division

Multi-step equations 64. -18 = 1 – 5 r + 6

Multi-step equations with variables on both sides Solve each equation. Solve algebraically for x. What is the value of x in the equation _______? Procedure: 1) Distribute and combine like terms (if needed) 2) Get all variable terms on one side and all numbers on the other side using addition/subtraction. 3) Solve for the variable by using multiplication/division. 66. -20 – 2 v = -8(-4 v – 2) – 2

Multi-step equations with variables on both sides 66. -20 – 2 v = -8(-4 v – 2) – 2

Slope (m) Find the slope of the line through each pair of points. What is the slope of the line passing through the points _____ and ______? Procedure: 1) Label your points x 1, y 1, and x 2, y 2 2) Use slope (m) formula: 3) Solve for m. (slope)

Slope (m) 73. (2, 4) and (7, 1)