course Mth 158
R.43. (x-2) (x^2+2x+4) = x^3+2x^2+4x-2x^2-4x-8= x^3-8
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6. True or False: (x+a)(x^2+ax+a)= x^3+a^3?x+a)(x^2+ax+a)= x^3+ax^2+ax+ax^2+a^2x+a^2= x^3+2ax^2+ax+ax^2+a^2x+a^2= x^3+3ax^2+ax+a^2x+a^2, so false
Tell whether the expression is a monomial. If it is, name the variable(s) and the coefficent and give the degree of the monomial.
9. 8/x..not a monomial 12.5x^2y^3..monomial, coefficient 5, degree 3
15.x^2+y^2..not a monomial
Tell whether the expression is a polynomial. If it is, give its degree.
18.1-4x..no 21.3x^2-5/x?ot a polynomial 24.10z^2+z..polynomial, degree,2
add,subtract,or multiply as indicated. Express your answer as a single polynomial in standard form.
27. (x^2+4x+5)+(3x-3)= x^2+(4x+3x)+2= x^2+7x+2 30. (x^2-3x-4)-(x^3-3x^2+x+5)= -x^3(x^2+3x^2)+(-3x-x)+(-4-5)= -x^3+4x^2-4x-9
33.(x^2-3x+1)+2(3x^2+x-8 ( 4 x^3 - 3 x^2 - 1 ) - 6 ( 4 x^3 + 8 x - 2 4)= (x^2-3x+1)+6x^2+2x-8)= (x^2+6x^2)+(-3x+2x)+(1-8)= 7x^2-x-7 36. 8 ( 4 x^3 - 3 x^2 - 1 ) - 6 ( 4 x^3 + 8 x ?2= (32x^3-24x^2-8)-24x^3-48x+12= (32x^3-24x^3)+(-24x^2)+(-8+12)-48x=8x^3-24x^2-48X+4 39. 9(y^2-3y+4)-6(1-y^2)= 9y^2-27y+36)+(-6+6y^2)= (9y^2+6y^2)+(-27y)+36-6)= 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^3+2x^2-4x)+(x^2+2x-4)= x^3+(2x^2+x^2)+(-4x+2x)-4= x^3+3x^2-2x-4
Multiply the polynomials using the FOIL method. Express your answer as a single polynomial in standard form.
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-x-5x+5= x^2-6x+5 57.(-2x+3)(x-4)=-2x^2+8x+3x-12= -2x^2+11x-12 60. ( 3 - x)? (-2x - 3) ( 3 - x)= -6x=2x^2-9+3x= -3x+2x^2-9= 2x^2-3x-9 63.(-2x-3y)(3x+2y)= -6x^2-4xy-3xy-6y^2= -6x^2-7xy-6y^2
Multiply the polynomials using the special product formulas. Express your answer as a single polynomial in standard form.
66. (x-1) (x+1) ) = x^2+x-x-1= x^2-1 69. (x+4) (x+4)= x^2+4x+4x+16=x^2+8x+16
72.(x-5)(x-5)=x^2-5x-5x+25= x^2-10x+25 75.(2x-3) (2x-3)= 4x-6x-6x+9=4x-12x+9
78.(x+3y)(x-3y)=x^2-3xy+3xy-9y^2=x^2-9y^2 81.(x+y)(x+y)=x^2+xy+xy+y^2=x^2+2xy+y^2 84. (2x + 3y)^2 = (2x+3y)*(2x+3y)=4x^2+6xy+6xy+9y^2= 4x^2+12xy+9y^2 87.(2x+1)^3= (2x+1) (2x+1) (2x+1)= 4x^2+2x+2x+1 (2x+1)= 4x^2+4x+1 (2x+1)= 8x^3+8x^2+2x+4x^2+4x+1= 8x^3+12x^2+6x+1
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This looks good. I haven't reviewed all the details but I've looked for common errors and don't see anything of concern--it's apparent that you know what you're doing here. Let me know if you have questions.