Please show steps Show all work necessary to display to the grader that you know
ID: 2840787 • Letter: P
Question
Please show steps
Show all work necessary to display to the grader that you know what you are doing Refer to the following polynomials f(x) = 3x - 4 g(x) = x + 2 h(x) = 2 - 3x2 j(x) = x3 + 8 Evaluate the following: f(x)+g(x) + h(x)+j(x) = (f(x)+h(x)) + (g(x)+j(x)) = h(x) middot j(x) = What is the degree of the polynomial h(x)? What is the leading coefficient of the polynomial f(x)? Perform the indicated operations and simplify completely. 5x2 - 3x(4 - 3(x - 2)) = (2a-3b)2 = (2x - y)(2x + y) - (2x - y)2 = (3x3 - 2y)2 = e. (x-2y)3 = Mark each statement as TRUE or FALSE. A natural number is a rational number. A number with a repeating decimal expansion is an irrational number. Simplify each expression completely. An expression is simplified when there are no parentheses, no powers raised to powers, each base appears once and only once, and only positive exponents should be used, a. 6(xy3)5 = 9u8x6/3u4x8 = (x-3y2)-2 = u5/3 u2/3 = (9a4b-2)1/2 = 5 degree / 32 + 3-2/2-2 = (x1/2 + y1/2)2 = (3x1/2-y1/z)(2x1/z + 3y, 1/z) = Factor the following polynomials completely, using integer coefficients only. If a polynomial cannot be factored further, using only integer coefficients, state so. 12x2 + 5x - 3 = 8x2 - 18xy + 9y2 = t2 - 4t - 6 =Explanation / Answer
1)
a)
= 3x- 4 + x + 2 + 2-3x^2 + x^3 + 8
= x^3 - 3x^2 + 4x + 8
b)
= (3x - 4 + 2-3x^2) - (x+2+x^3+8)
= 2x - 3x^2 - x^3 - 12
= -x^3 - 3x^2 + 2x - 12
c)
= (2-3x^2)(x^3+8)
= 2x^3 + 16 - 3x^5 - 24x^2
= -3x^5 + 2x^3 - 24x^2 + 16
d)
degree = 2
e)
= 3
2)
a)
5x^2 - 3x(4-3(x-2)) = 5x^2 - 3x(4-3x+6)
= 5x^2 - 3x(10-3x)
= 5x^2 - 30x+9x^2
= 14x^2 - 30x
b)
(2a - 3b)^2 = 4a^2 + 9b^2 - 12ab
c)
(2x-y)(2x+y) - (2x-y)^2 = 4x^2- y^2 - 4x^2-y^2 + 4xy
= - 2y^2 + 4xy
d)
(3x^3 - 2y)^2 = 9x^6 + 4y^2 - 12x^3 y
e)
(x-2y)^3 = x^3 - 6x^2 y + 12xy^2 - 8y^3
3)
a) False
b) False
4)
a) 6(xy^3)^5 = 6(x^5)(y^3)^5 = 6x^5 y^15
b)
9u^8x^6/(3u^4x^8) = 3u^8x^6/(u^4x^8)
= u^(8-4) /x^(8-6)
= u^4 / x^2
c)
(x^-3 y^2)^(-2) = (x^-3)^(-2) (y^2)^(-2)
= x^(6) y^(-4)
= x^(6) /y^(4)
d)
u^(5/3) u^(2/3) = u^(5/3 + 2/3) = u^(7/3)
e)
(9a^4 b^(-2))^(1/2) = 3 a^2 / b
4)
f)
5^0 /3^2 + 3^(-2) /2^(-2) = 1/9 + 2^(2) /3^(2)
= 1/9 + 4/9
= 5/9
g)
(x^(1/2) + y^(1/2))^2 = x + y + 2x^(1/2) y^(1/2)
h)
(3x^(1/2) - y^(1/2) )*(2x^(1/2) + 3y^(1/2) ) = 6x - 3y + 7x^(1/2) y^(1/2)
5)
a)
12x^2 + 5x - 3 = (3x - 1)(4x + 3)
8x^2 - 18xy + 9y^2 = (2x - 3y)(4x - 3y)
t^2 - 4t - 6 =
can not be factored