course MTH 158
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College Algebra
Asst. 5
3. (x-2)(x^2 + 2x + 4) = x^3 + -4 + -4 = -8
6. True (x+a)(x^2 + ax + a) = x^3 + a^3
Tell whether the expression is a monomial. If it is, name the variables and
the coefficients and five the degree of the monomial
9. 8/x is not a monomial
12. 5 x^2y^3 Yes it is monomial 5 is the coefficient -
2 and 3 the degrees - x, y are the variables
15. x^2 + y^2 It is not a monomial because the two terms are separated
by a plus sign
Tell whether expression is polynomial - Give it's degree
18. 1 - 4x It is a polynomial, but it has no degree
21. 3x^2 - 5/x not a polynomial
24. 10z^3 + z not a polynomial
Express answer as a single polynomial in standard form. Add, subtract,
and multiply as stated.
27. (x^2 + 4x + 5) + (3x-3) = x^2 + 7x + 2
30. (x^2 - 3x + 4) - (x^3 - 3x + x + 5) = -x^3 + 4x^2 - 4x - 9
33. (2^2 - 3x + 1) + 2(3x^2 + x-4)
= x^2 - 3x + 1 + 6x^2 + 2x - 8 = 7x^2 - 1x - 7
36. 8(4x^3 - 3x^2 - 1) - 6(4x^3 + 8x -2)
= (32x^3 - 24X^2 -8) - (24x^3 + 48x -12)
=56x^3 - 24x^2 -4
39. 9(y^2 - 3y + 4) - 6(1-y^2)
=9y^2 - 27y + 36 - 6 - 6y2
=15y^2 - 27y + 30
42. 4x^2(x^3 - x + 2)
=4x^5 - 4x^3 + 8x^2
45. (x+1)(x^2 + 2x - 4)
=x(x^2+2x-4)+1(x^2+2x-4)
=x^3 + 2x^2 - 4x + x^2 + 2x - 4
=x^3 + 3x^2 - 2x -4
Multiply polynomials suing foil method.
48. (x+3)(x+5) = x^2 + 5x + 3x + 15 = x^2 + 8x + 15
51. (x-4)(x+2) = x^2 + 2x -4x - 8 = x^2 + 2x - 8
54. (x-5)(x-1) = x^2 - 1x - 5x - 5 = x^2 - 4x - 5
57. (-2x + 3)(x-4) = -2x^2 + 8x + 3x -12 = -2x^2 + 11x - 12
60. (-2x -3)(3-x) = -6x - 2x - 9 + 3x = -7x -9
63. (-2x - 3y)(3x + 2y) = -6x^2 - 4xy - 9xy - 6y^2
=6x^2 - 13xy - 6y^2
Multiply polynomials using special products formulas.
66. (x-1)(x+1) = x^2 + 1x - 1x - 1 = x^2 + 2x - 1
69. (x+4)^2 = x^2 + 8x + 16
72. (x-5)^2 = x^2 - 25
75. (2x-3)^2 = 2x^2 - 2(2x)(3) + 3^2 = 4x^2 - 12x + 9 =
-8x^2 + 9
78. (x+3y)(x-3y) = x^2 + 3xy + 3xy - 9y = x^2 + 6xy - 9y
81. (x + y)^2 = x^2 + 2xy + y^2
84. (2x + 3y)^2 = 2x^2 + 5xy^2
87. (2x+1)^3 = 2x^3 + 3(2x)^2(1)+3(2x)1 = 8x^3 + 12x^2 + 6x + 1
90. ????????
93. I like to use the FOIL method because when I work a problem, I need to
see why we do the steps we need to do. It is easier for me to see this when
I use this method.
The problem with FOIL is that it doesn't work with anything longer than a binomial, which is why I stress the distributive law.
However as long as you clearly understand how to use the distributive law, FOIL is a legitimate shortcut.
I can't check every detail of every solution--the Query is designed to give me a more detailed picture of your thinking and to pinpoint details--but I did scan your work and you are clearly doing things correctly, overall.
One error I did spot:
#60: (-2x -3)(3-x) = -6x - 2x^2 - 9 + 3x, not -6x - 2x - 9 + 3x