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MATH 21 Lecture Notes - Lecture 3: Greatest Common Divisor, Quotient Rule

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13 Oct 2018

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MATH 21 verified notes

MATH 21 Lecture Notes - Lecture 1: Exponentiation, Quotient Rule, Product Rule

MATH 21 Lecture Notes - Lecture 3: Greatest Common Divisor, Quotient Rule

Document Summary

Math 21 - chapter 4,5 division/ factoring: dividing a polynomial by a monomial, coefficient divide coefficient; variables divide variables. Example: (cid:886)(cid:1876)(cid:2872) (cid:889)(cid:1876)(cid:2871)+(cid:883)(cid:884)(cid:1876)(cid:2870) (cid:886)(cid:1876)(cid:2871) (cid:1876) (cid:2875)(cid:2872)+(cid:885)(cid:1876) (cid:2869) (cid:1876) (cid:2875)(cid:2872)+(cid:2871: place (cid:882)(cid:1876),(cid:1866) (cid:1871) (cid:1866)(cid:1872)(cid:1857)(cid:1857)(cid:1870) (cid:1867)(cid:1866) (cid:1853)(cid:1866)(cid:1877) (cid:1865)(cid:1871)(cid:1871)(cid:1866) (cid:1856)(cid:1857)(cid:1870)(cid:1857)(cid:1857) Example: (cid:883)(cid:882)(cid:882)(cid:1865)(cid:2873) (cid:887)(cid:882)(cid:1865)(cid:2872)+(cid:884)(cid:887)(cid:1865)(cid:2871) (cid:884)(cid:887)(cid:1865)(cid:2871) (cid:4666)(cid:886)(cid:1865)(cid:2870) (cid:884)(cid:1865)+(cid:883)(cid:4667: first thing always: greatest common factor (gcf, factoring, factor by grouping, when there are 4 terms. There is no gcf for all 4 terms, so we break it down and. Example: kn-m-k+mn find common factors for each 2 terms: (kn-k)+(mn-n) k(n-1)+m(n-1) (k+m)(n-1: factor quadratics when a is 1 first term of the trinomial: b, (cid:1853)(cid:1876)(cid:2870)+(cid:1854)(cid:1876)+(cid:1855) Example: (cid:1854)(cid:2870) (cid:889)(cid:1854)+(cid:883)(cid:882) (cid:4667) (cid:4667)(cid:4666)(cid:1854) (cid:4666)(cid:1854) (cid:4666)(cid:1854) (cid:884)(cid:4667)(cid:4666)(cid:1854) (cid:887)(cid:4667: (cid:1853)(cid:1876)(cid:2870)+(cid:1854)(cid:1876)+(cid:1855), (cid:1857)(cid:1872) (cid:1867)(cid:1856) Example: (cid:888)(cid:1876)(cid:2870) (cid:883)(cid:891)(cid:1876)+(cid:883)(cid:882: factor quadratics when a is other than 1. The first terms of the two binomials are square roots of the. Find two factors that multiply to 10, add to -7: -2 and -5. Find two factors that multiply to 60, add to -19: -15 and -4.

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Related Questions

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1. Factor out the GCF from thepolynomial.
20m^9 + 6m^7 + 20m^5

2(10m^9 + 3m^7 +10m^5)
No common factor
m^5 (20m^4 + 6m^2 +20)
2m^5 (10m^4 + 3m^2 +10)

2. Find the solution to the system by addition(elimination) method.
4x + 15y = 15
8x - 3y = -3

(1, 0)
(0, 0)
(0, 1)
(1, 1)

3. (11p + 4)(11p - 4)

p^2 - 16
121p^2 + 88p - 16
121p^2 - 16
121p^2 - 88p -16

4. Find the solution to the system by addition(elimination) method.
2x + 15y = -91
9x + 5y = 28

(-5, 7)
(7, -7)
(9, -9)
(-7, 7)

5. Factor by grouping.
18x^3 + 15x^2 + 12x + 10

(3x^2 + 2)(6x + 5)
(18x^2 - 2)(x - 5)
(3x^2 - 2)(6x - 5)
x(18x + 2)(x +5)

6. (x + 3y)(x + 5y)

x^2 + 5xy + 15y^2
x^2 + 8xy + 8y^2
x^2 + 8xy + 15y^2
x + 8xy + 15y

7. 6x^7 (9x^7 + 12x^2 - 7)

54x^7 + 72x^2 - 42
54x^14 + 72x^9
54x^14 + 72x^9 -42x^7
54x^14 + 12x^2 -7

8. 15x^2 - 12x + 10x - 8

(15x + 2)(x - 4)
(15x - 2)(x + 4)
(3x - 2)(5x + 4)
(3x + 2)(5x -4)

9. For the polynomial, state the degree andwhether or not the polynomial is a monomial, a binomial, or atrinomial.
5x^3y^4 - 8x^5y^6 + 8

Binomial, degree 7
Trinomial, degree 3
Trinomial, degree18
Trinomial, degree11

10. (3x^8 + 2x^7 - 4x^6 + 8) + (7x^8 - 4x^7 +8x^6 + 1)

10x^8 - 2x^7 + 4x^6 +9
12x^42 + 9
10x^26 - 2x^14 + 4x^12 +9
4x^8 + 4x^7 + 4x^6 +9

11. (2n^5 - 3n^3 - 6) - (5n^5 - 14n^3 -3)

-3n^5 + 2n^3 - 9
-3n^5 + 11n^3 - 3
5n^8
-3n^5 + 11n^3 -9

12. Use the substitution method to solve thesystem.
x - 4y = -13
7x - 5y = -22

(1, 4)
(-2, 4)
(-1, 3)
No solution

13. Use the substitution method to solve thesystem.
8x - 6y = 32
2x - 2y = 8

(3, 1)
(4, 1)
(4, 0)
No solution

14. Terms in a polynomial are separated byaddition or subtraction.

15. A polynomial is an algebraic expression ofone or more terms.

16. A solution of two linear equations in twovariables is an ordered pair that is a solution to eachequation.

17. The greatest common factor will always begreater than the largest factor of each term of theexpression.

18. A system of equations in two variables mayhave infinite solutions.

19. When two or more algebraic expressions aremultiplied, each expression is called a term.

20. Factoring is multiplication inreverse.