Math 7

2. MATHEMATICS 7
Ms. Ederliza B. Pineda
Engr. Virgilio V. Dionisio
Memorial High School

3. MATH
Motivated
Attentive
Happy
Thinking critically
Always remember to be MATH!

4. Identify what kind
of polynomial is each
according to the
number of terms.

5. 1. 3x2y – 4z
binomial

6. 2. 25x3yz
monomial

7. 3. 2m+n-p+5q
multinomial

8. 4. 2c
monomial

9. 5. 7x2-9x+2
trinomial

10. 6. 10m2n2 + 1
binomial

11. 7. a2 – 16
binomial

12. 8. a-2b+3c-4
multinomial

13. 9. 100a2b5c3
monomial

14. 10. 9x2+12xy+4y2
trinomial

15. Most Essential Learning
Competency:
The learner evaluates
algebraic expressions and
perform operations on
polynomials (addition and
subtraction).
Code: M7Al-IIc-4, M7Al-IId-2

16. At the end of the learning period,
you are expected to:
1. evaluate algebraic expressions
2. perform addition and subtraction
on polynomials

17. Lesson:
Polynomials

18. Standard Form
The polynomial is arranged from
the term with the highest degree, up
to the term with the lowest degree.
Examples:
a. 10m5 +m4 -12m3 +6m2 –m +1
b. 8x4y3 +x3y2 –x2y +11

19. Write the polynomial in standard form.
10b5 +2b7 -11b4 +6b2 –25 +b
Answer:
2b7 +10b5 -11b4 +6b2 +b –25

20. Write the polynomial in standard form.
3x2y3 +2x4y4 + 7x2 -4 +y
Answer:
2x4y4 +3x2y3 + 7x2 +y -4

21. Degree of Polynomial
The exponent or the sum of the
exponents of the variable in the
leading term.
Examples:
a. 10m5 +m4 -12m3 +6m2 –m +1
b. 8x4y3 +x3y2 –x2y +11

22. Leading Term
The first term in a polynomial
written in standard form.
Examples:
a. 10m5 +m4 -12m3 +6m2 –m +1
b. 8x4y3 +x3y2 –x2y +11

23. What is the degree of the polynomial?
2b7 +10b5 -11b4 +6b2 +b –25
Answer: 7
What is the leading term?
Answer: 2b7

24. What is the degree of the polynomial?
3x2y3 +2x4y4 + 7x2 -4 +y
Answer: 8
2x4y4 +3x2y3 + 7x2 +y -4
What is the leading term?
Answer: 2x4y4

25. Leading Coefficient
The numerical coefficient of the
leading term.
Examples:
a. 10m5 +m4 -12m3 +6m2 –m +1
b. 8x4y3 +x3y2 –x2y +11

26. Kinds of Polynomial according to
degree:
a) Constant –a polynomial of degree zero
b) Linear –degree one
c) Quadratic –degree two
d) Cubic –degree three
e) Quartic –degree four
f) Quintic –degree five
The next degrees have no universal name
yet, they are called “polynomial of degree __”

27. Lesson:
Evaluating
Algebraic Expressions

28. How do we evaluate
algebraic expressions?

29. Ex. 1 Evaluate: 5m3 – 3m +4,
when m= 1
Solution:
5m3 – 3m +4
=5(1)3 – 3(1) +4
=5 –3 +4
=2 +4
=6

30. Ex. 2 Evaluate: 5m3 – 3m +4,
when m= -2
Solution:
5m3 –3m +4
=5(-2)3–3(-2) +4
=5 (-8)+6 +4
= -40+6+4
= -30
= -34+4

31. Ex. 3 Find the value of: 4x – 6y
3x+y
when x=3 and y=0
Solution:
4x – 6y
3x+y
= 4(3)– 6(0)
3(3)+0
= 12
9
4
3
=

32. Ex. 4 Find the value of: 4x – 6y
3x+y
when x=-2 and y=4
Solution:
4x – 6y
3x+y
= 4(-2)– 6(4)
3(-2)+ 4
=16
= -8 – 24
-6 + 4
= -32
-2

33. Try this!
Evaluate the
given algebraic
expressions.

34. 1 x + 2y when x=3 and y=1
2x+y
Solution:
x + 2y
2x+y
= 3 + 2(1)
2(3)+1
= 3 + 2
6 + 1
5 .
7
=

35. 2 4a3–2a2+5a–3, when a=2
Solution:
4a3–2a2+5a–3
=4(2)3–2(2)2+5(2)–3
= 31
=
=4(8)–2(4)+10–3
=32–8+10–3
=24+10–3
=34 – 3

36. Lesson:
Adding and Subtracting
Polynomials

37. How do we add or
subtract polynomials?

38. Remember!
Only LIKE
TERMS can be
combined or
simplified.

39. LIKE TERMS are
terms with the
same variables
and exponents

40. Identify whether the
given are LIKE
TERMS or NOT.

41. 3m2
NOT
3m

42. 2xy
LIKE TERMS
5xy

43. 4b2 20b2
LIKE TERMS

44. 2x2y
NOT
4xy

45. 10n
NOT
10

46. Add/Subtract the given
polynomials.
EXAMPLES

47. (2x+1) + (3x +5)
= 5x + 6

48. (4m2-3m +5)+(7m2-2m -3)
= 11m2 - 5m +2

49. (15b+8) - (5b+6)
= 10b + 2

50. (4y2+10y+2) - (y2+7m-3)
= 3y2 +3y +5

51. (2x2+9) + (3x +1)
= 2x2 +3x +10