SOLUTION: 1.)Factor x� - 4x + 4 � 9y�. 2.)The volume of a rectangular prism is represented by the polynomial 2x3 - 24x2 + 72x. (a) Factor the polynomial completely. (b) If x represents 8

Question 321651: 1.)Factor x� - 4x + 4 � 9y�.
2.)The volume of a rectangular prism is represented by the polynomial 2x3 - 24x2 + 72x.
(a) Factor the polynomial completely.
(b) If x represents 8 cm, what are the possible dimensions of the prism?
(c) Could x represent 5cm? Explain.
3.)x4 + 22x2 + 121
Found 2 solutions by mananth, toidayma:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
1.)Factor x� - 4x + 4 � 9y�.
..
(x+2)^2-9y^2
(x+y+3y)(x+y-3y)
(x+4y)(x-2y)
2.)The volume of a rectangular prism is represented by the polynomial
2x3 - 24x2 + 72x.
(a) Factor the polynomial completely.
2x(x^2-12x+36)
2x(x^2-6x-6x+36)
2x(x(x-6)-6(x-6))
2x(x-6)^2
(b) If x represents 8 cm, what are the possible dimensions of the prism?
(c) Could x represent 5cm? Explain.
2x(x-6)^2
16(6)^2
16*36
find the factors for various dimensions

3.)x4 + 22x2 + 121
x^4+2*11*x^2+121
= (x+11)^2

Answer by toidayma(44) (Show Source): You can put this solution on YOUR website!
1. x� - 4x + 4 � 9y� = (x-2)^2 - (3y)^2 = (x - 2 - 3y)(x - 2 + 3y)
2. V(x) = 2x3 - 24x2 + 72x
a. V(x) = 2x(x^2 - 12x^2 + 36) = 2x*(x-6)^2 = 2x*(x-6)*(x-6)
b. V(x) = 2x*(x-6)*(x-6), this suggests that the three dimensions of the rectangular prism are either {2x, (x-6), and (x-6)} or {x, (x-6) and 2(x-6)}.
With x = 8, we have two possibility {16, 2, 2) or {8, 2, 4}.
c. Since (x-6)^2 = (6-x)^2 = (6-x)(6-x), therefore x can represent 5. In this case, the possible dimensions of the prism are {10, 1, 1} or { 5, 2, 1}.
3. x^4 + 22x^2 + 121 = (x^2 + 11)^2.
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