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MAC 1105 Lecture Notes - Lecture 2: Greatest Common Divisor, Quadratic Formula

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School
HCC
Department
Mathematics: Calculus and Pre-Calculus
Course
MAC 1105
Professor
Pantelis

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Document Summary

Set each component on the left equal to zero. 2x - 1 = 0 (add 1 to both sides) Add 2 to both sides. x2 = 3 x-2 = (cid:888) x = (cid:885) x = 2 (cid:888) Step 3 take 1/2 of b, then square the result. (1/2 b)2. Step 5 you now have a perfect square on the left. Solve for x2 - 6x + 4 = 0 a=1; b=-6; c=4. Identify a, b, and c. set the equation equal to c. x2 - 6x = -4 (1/2 b)2 = ((cid:1005)/(cid:1006) -6)2 = -32 = 9. Add this to both sides. x2 - 6x + 9 = -4 + 9. Take the left side an make it a squared binomial. Simplify the right. (x - 3)2 = 5. Solve for x. x = 3 = x - 3 = (cid:887) Identify a, b, and c. a=2, b=-6, c=1.

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Related Questions


Show transcribed image text

For the best rating please complete by answering all thequestions in one post so I could rate you once you post.

Answers must be correct in order to get best rating.


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.
True
False


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


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


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


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


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


20. Factoring is multiplication inreverse.
True
False

**the text is what is contained in the picture**

1. Consider first a linear equation: 3x – 1 = 5.

a. Use a graphing utility to show y1= 2x – 1 and y2=5 and determine the point of intersection. Make a sketch and label it.

b. How does the graph in part (a) relate to the solution set of the equation 3x – 1 = 5?

c. To solve the equation 3x – 1 =5 algebraically, the first step is to add 1 to both sides of the equation. Use a graphing utility to show y1=3x and y2=6, and determine the point of intersection. Make a sketch and label it. How does this graph relate to the equation 3x=6?

d. The final step to solve the equation is to divide both sides of the equation by 3. Use a graphing utility to show y1=x and y2=2, and determine the point of intersection. Make a sketch and label it. How does this graph relate to the equation x=2?

e. The algebraic steps to solve the equation 3x – 1 = 5 produce two equations: 3x=6 and x=2. How do the graphs you sketched above represent the fact that these equations are equivalent to the original?