FACTORING.pptxgrade 8 mathematics powerp

factoring

1. INTEGERS

2. What is an Integer?

3. An integer is a positive or negative whole number, including 0. …-3, -2, -1, 0, 1, 2, 3…

4. There are “4” Integer Operations

5. Addition + Subtraction - Multiplication x Division ÷

6. 5 - 6 = -3 + 2 = 6 + 5 = -8 + 7 = 9 - 9 =

7. 5 + (-1) = 4 5 – (-1) = 6 5 + (+5) = 10

8. 4 – (-5) = 9 + (-7) = 6 – (+2) = 8 – (-7) = 9 + (+3) =

9. 5 + (-2) = 3 – (-4) = 1 – (+2) = 5 – (-3) = 7 – (-6) =

10. Factoring Polynomials

11. The Greatest Common Factor Factoring Trinomials of the Form x 2 + bx + c Trinomials of the Form ax 2 + bx + c Factoring Trinomials of the Form x 2 + bx + c by Grouping Factoring Perfect Square Trinomials and Difference of Two Squares COMPETENCIES

12. The Greatest Common Factor

13. Factors (either numbers or polynomials) When an integer is written as a product of integers, each of the integers in the product is a factor of the original number. When a polynomial is written as a product of polynomials, each of the polynomials in the product is a factor of the original polynomial. Factoring – writing a polynomial as a product of polynomials.

14. Greatest common factor – largest quantity that is a factor of all the integers or polynomials involved. The Greatest Common Factor Finding the GCF of a List of Integers or Terms Prime factor the numbers. Identify common prime factors. Take the product of all common prime factors. If there are no common prime factors, GCF is 1.

15. Find the GCF of each list of numbers. 12 and 8 12 = 2 · 2 · 3 8 = 2 · 2 · 2 So the GCF is 2 · 2 = 4. 7 and 20 7 = 1 · 7 20 = 2 · 2 · 5 There are no common prime factors so the GCF is 1.

16. Find the GCF of each list of numbers. 6, 8 and 46 6 = 2 · 3 8 = 2 · 2 · 2 46 = 2 · 23 So the GCF is 2. 144, 256 and 300 144 = 2 · 2 · 2 · 3 · 3 256 = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 300 = 2 · 2 · 3 · 5 · 5 So the GCF is 2 · 2 = 4.

17. Find the GCF of each list of terms. 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 6 x 5 and 4 x 3 6 x 5 = 2 · 3 · x · x · x 4 x 3 = 2 · 2 · x · x · x So the GCF is 2 · x · x · x = 2 x 3

18. If no sides of a triangle are equal, then the triangle is classified as ______________.

19. What is the measure of the angle which is the complement of an angle measures 48 o ?

20. Two nonadjacent angles formed by two intersecting lines are called ____ angles.

21. What property is illustrated in the statement, “If ∠ A ≅ ∠ B , ∠ B ≅ ∠ C then ∠ A ≅ ∠ C” ?

22. Which triangle is congruent to Δ CDF?

23. A star in the sky represents a __________ .

24. What additional information is needed to prove that ΔLPM and ΔOPN are congruent by SAS postulate?

25. Which triangle is congruent to Δ FDC?

26. Which triangle is congruent to Δ LPM ?

27. If two legs of one triangle is congruent to the two legs of another triangle, then the triangles are congruent by what theorem?

28. What are the three undefined terms in mathematical system?

29. What additional information is needed to prove that ΔLPM and ΔOPN are congruent by SSS postulate?

30. Using the distributive property, 4( a+b ) =________________. 4a + b b. b + 4a c. 4a + 4b d. 4 + a + b

31. If the hypotenuse and an acute angle of one triangle is congruent to the hypotenuse and an acute angle of another triangle, then the triangles are congruent by what theorem?

32. An angles whose sum is equal to 180 ?

33. Angle C and E are supplementary angles, if m<C = 78 o , find m < E.

34. The property of equality which justifies that if MN = MN, then MN = MN?

35. The property of equality which justifies that if M = N, then N = M?