Factor completely 1 x' - x - 2 = 2 y2 - 12y + 36 = 3 Zz - 16 = 4 x- + 4x +4 = 5 x3 - 8x- + 12x = 6 2x3 - 2x2 - 40x =\f11 x4 - 13x2 + 36 = 12 x - 12x* + 48x2 - 64 = 13 The volume of a rectangular prism is modeled by the function V(x) = x3 - 8x2 + 19x - 12, which is graphed on the right. Identify the values of x for which V (x) = 0, and use the graph to factor V(x). 2 V(x) = 14 Given the Base and height of the hexagonal prism, find the volume in terms of x. (hint: V = Bh) h - r+) B= x3 - 2x2 + 4x - 815 What is the volume of the W= X 4 rectangular prism in terms of x. V = h = 2x |1 1 = 3xPut the following polynomials into standard form. 1 3a2+2a4a3+5) 2 652+2b45+b 3 8c 4 5:33 9 4 3d2+2d4d3+5 9 Simply and put into standard form. [6x2 ?x+8) + [4352 +9x5) = (4m2 m+2} (3m+ 10m2 4) = (93g2)(29+392+4) = [4y+y2+9)+(3y26y+y39)= (2&35a2+B)(4aa33)= LDDO'HJO'HU'I 10 (Elk 12} + [4 + 9k) (3ft: 8) = 11 Find the measure of the third side of this triangle with a perimeter of 4x~ + 4x + 3. 4x2 - 2 ?= 2x - 1 12 Find the measure of the fourth side of this trapezoid with a perimeter of 3x2 + 12x + 7. 2x2 + 3 7 = 3x +4Use long division or synthetic division. x-+x-1 1 x-1 2 (3x]- 11x2 - 56x - 48) + (3x + 4) = 3 y +yz+20 = 4 (m3 + 10m' + 31m + 30) + (m + 5) = 60-16d2+04 5 10-d2 6 (13 - 7k2 + 12k) + (k2 - 3k) = 2x--5x+2 7 = Nj 8 (Baz + 9) + (4a + 2) = 9 4x-+3x3+10 x-2 10 (g* + 693+ 692) + (g +5) =11 A rectangle has an area of 2x - 8x2 + 2x + 12. The width of the rectangle is x - 2. What is the length of the rectangle? 12 A new experimental electrical system has a voltage that can be modeled by the function V(t) = 0.5t*+ 4.5t + 4t, where t represents time in seconds. The resistance in the system also varies and can be modeled by R(t) = t + 1. The current / is related to voltage and resistance by the equation / =-. Now find the expression that represents the current in the system. 13 The Van de Graaff generator is a machine that produces very high voltages by using small, safe levels of electric current. One machine has a current that can be modeled by /(t) = t + 2, where t > 0 represents time in seconds. The power of the system can be modeled by P(t) = o.5t#+ 6t* + 10t. Write an expression that represents the voltage of the system. The voltage | is related to current / and Power P by the equation = =