 = -450*y**3 + 30021*y**2 - 6491*y - 2171. Let r(a) = -226*a**3 + 15011*a**2 - 3245*a - 1085. Let q(z) = 3*l(z) - 5*r(z). Let q(v) = 0. Calculate v.
-2/11, 2/5, 68
Let j(c) = -130*c + 2. Let i be j(-1). Suppose -17 = -l + i. Factor 78*o + l - 5*o**2 - 649 + 22*o.
-5*(o - 10)**2
Let n(z) be the second derivative of -40/3*z**4 + 16/3*z**6 - 28*z - 19/5*z**5 + 2/3*z**7 + 0*z**2 + 8*z**3 + 2. Let n(m) = 0. What is m?
-6, -1, 0, 2/7, 1
Let t be (0/3 - (-22)/(-132))*0. Let k(f) be the third derivative of -5/6*f**3 + 1/42*f**7 - 1/12*f**6 + 0*f**5 + 0 - 16*f**2 + t*f + 5/12*f**4. Factor k(x).
5*(x - 1)**3*(x + 1)
Let q(y) = y**4 - 1. Let n(z) = 16*z**4 + 32*z**3 + 176*z**2 + 384*z + 274. Let h(f) = 2*n(f) - 28*q(f). Factor h(g).
4*(g + 2)**2*(g + 6)**2
Let l(f) be the first derivative of -f**5/90 - 13*f**4/36 - f**2/2 - 87*f + 3. Let x(q) be the second derivative of l(q). Factor x(s).
-2*s*(s + 13)/3
Factor 3/2*d - 7/3 - 1/6*d**2.
-(d - 7)*(d - 2)/6
Let h(f) be the second derivative of -f**5/210 + 43*f**4/42 - 8*f**3 + 500*f**2/21 + 2*f + 2604. Factor h(z).
-2*(z - 125)*(z - 2)**2/21
Factor 25088/15 - 448/15*o + 2/15*o**2.
2*(o - 112)**2/15
Let h = 127/582 - -7513/2910. What is m in -108/5*m**2 + 28/5 - h*m**3 - 66/5*m = 0?
-7, -1, 2/7
Let w(b) be the second derivative of b**7/98 - b**6/10 + 51*b**5/140 - 17*b**4/28 + 3*b**3/7 + 1400*b. What is k in w(k) = 0?
0, 1, 2, 3
Let j = 1512764/52423 - -2/7489. Let f = 206/7 - j. Factor -24/7*r - f*r**2 + 0.
-4*r*(r + 6)/7
Let u(r) be the third derivative of -r**5/240 - 1067*r**4/96 + 1069*r**3/12 + 207*r**2 - 3*r. Find j such that u(j) = 0.
-1069, 2
Let k be (-1)/(10/(-2)) + (-3)/165*11. Factor k + 38/5*y - 2/5*y**2.
-2*y*(y - 19)/5
Let i = 16690 - 16687. Determine f, given that -60 - 84*f**i - 84/5*f**4 - 912/5*f**2 - 6/5*f**5 - 174*f = 0.
-5, -2, -1
Suppose -b + 1 = 0, -5*f + 9*f - 71 = b. Factor -1381*t**2 - 6 + 1376*t**2 + f*t + 42*t + 71.
-5*(t - 13)*(t + 1)
Let q = -775 + 787. Suppose 5*a = -13*s + 8*s - 15, a - 4*s = q. Factor -2/11*h**2 - 6/11*h + a.
-2*h*(h + 3)/11
Let b = 2171 + -2166. Let g(m) be the first derivative of 27/4*m**4 + 5 + 7*m**3 + 1/2*m**6 + 3*m**b + 3*m**2 + 0*m. What is l in g(l) = 0?
-2, -1, 0
Let j(m) be the second derivative of 4 + 2*m - 4*m**2 - 58/21*m**3 - 2/21*m**4. Determine z, given that j(z) = 0.
-14, -1/2
Let u(s) be the third derivative of -s**5/20 - 237*s**4/4 + 29*s**2 + 22*s. Factor u(k).
-3*k*(k + 474)
Let h(q) = -14*q**5 - 6*q**4 + 44*q**3 + 220*q**2 - 436*q. Let y(c) = 3*c**5 - 2*c**4 - 2*c**3 - c**2 + c. Let o(l) = h(l) + 4*y(l). Let o(k) = 0. Calculate k.
-6, 0, 2, 3
Let d(g) = 2*g**2 + 4*g + 2. Let n(k) = 5*k**2 - 2*k + 2. Let j(z) = -d(z) + n(z). Factor j(y).
3*y*(y - 2)
Let 3516*k + 2*k**2 + 974699 - 68929 + 639512 = 0. What is k?
-879
Factor -288 - 669*s - 270 + 35*s**3 - 366*s**2 - 48*s**3 - 1935*s + 166.
-(s + 14)**2*(13*s + 2)
Suppose 9*f + 6 - 114 = 0. Factor 7*c**2 - 11*c**2 + c**2 - f*c.
-3*c*(c + 4)
Let u(o) = -9*o**2 - 1961*o + 4182. Let x be u(-220). Factor 6/7*i**x + 2/7*i**3 - 6/7 - 2/7*i.
2*(i - 1)*(i + 1)*(i + 3)/7
Suppose 8 + 12 = 5*v. Suppose 0 = t + a - 16, 0 = -3*a + v*a. Let -4*w**2 + 158 + 0*w**2 - 174 - t*w = 0. What is w?
-2
Let q be 4355/26*15/(-1825). Let r = 9/73 - q. Factor 3 + 9/2*f + r*f**2.
3*(f + 1)*(f + 2)/2
Factor 4*x**2 + 126 + 1/2*x**3 - 261/2*x.
(x - 12)*(x - 1)*(x + 21)/2
Let w be (-1)/(-2)*(10 - (-1036)/(-105)). Let y(r) be the second derivative of 0*r**2 + 7/100*r**5 + 8*r + 0 + w*r**3 - 3/20*r**4. Solve y(s) = 0 for s.
0, 2/7, 1
Let x(r) be the second derivative of 7*r - 529/24*r**3 - 1/240*r**5 + 12167/24*r**2 + 0 + 23/48*r**4. Find p, given that x(p) = 0.
23
Let t(m) be the first derivative of 2 - 3/10*m**5 - 1/12*m**6 - 1/4*m**4 + 1/3*m**3 + 1/2*m + 3/4*m**2. Factor t(i).
-(i - 1)*(i + 1)**4/2
Let q(u) be the second derivative of u**5/100 + 6*u**4/5 + 113*u**3/10 + 134*u**2/5 + 6042*u. Factor q(a).
(a + 1)*(a + 4)*(a + 67)/5
Let j(w) be the third derivative of -w**5/570 + 61*w**4/228 + 292*w**3/19 - 2*w**2 + 152*w. Suppose j(a) = 0. Calculate a.
-12, 73
Let x(f) be the first derivative of -9/11*f**2 + 133 - 4/11*f**3 - 1/11*f**6 + 6/11*f**4 + 12/11*f + 0*f**5. Suppose x(w) = 0. Calculate w.
-2, -1, 1
Suppose -1459 + 31010*b + 16188 + 17792*b**2 - 29 + 2*b**5 + 1356*b**3 - 84*b**4 - 40*b**4 = 0. Calculate b.
-6, -1, 35
Let g(h) = 5*h**5 + 11*h**4 + 12*h**3 + 22*h**2 + 16*h. Let x be (-2)/4*(-12)/24*-4. Let j(r) = r**5 + 2*r**4 - r**2. Let v(z) = x*g(z) + 6*j(z). Factor v(i).
i*(i - 4)*(i + 1)*(i + 2)**2
Let m be 83/9 + (-60)/270. Factor -g**3 - 118*g**2 - 90 + 3*g**4 + g**4 + 2*g**4 + 192*g + m*g**3 + 2*g**4.
2*(g - 1)*(g + 5)*(2*g - 3)**2
Suppose -8/11*g**3 + 51/11*g**2 - 18/11*g + 0 = 0. Calculate g.
0, 3/8, 6
Let x(p) be the second derivative of p**6/24 + 5*p**5/4 - 55*p**4/8 + 85*p**3/6 - 23*p**2 - 23*p. Let s(i) be the first derivative of x(i). Solve s(z) = 0.
-17, 1
Let p = -22582 + 45165/2. Find u, given that 3*u + p*u**2 + 4 = 0.
-4, -2
Suppose 3*u = 4*t - 4027, 2*u - 2378 = -4*t + 1664. Let s = -1009 + t. Factor s - 3/4*n + 1/4*n**2.
n*(n - 3)/4
Factor -10*y**2 - 84*y - 5132552 + 90*y**2 + 5132552 + 100*y**3.
4*y*(5*y - 3)*(5*y + 7)
Let t(f) be the third derivative of 0*f**4 - 3/70*f**7 + 0*f + 0*f**3 + 7/12*f**6 - 5*f**2 + 4/15*f**5 + 0. Determine q so that t(q) = 0.
-2/9, 0, 8
Let x(d) = 7*d**4 + 2746*d**3 + 8092*d**2 + 8070*d + 2693. Let a(t) = -2*t**4 - 916*t**3 - 2697*t**2 - 2690*t - 898. Let h(v) = 8*a(v) + 3*x(v). Factor h(f).
5*(f + 1)**3*(f + 179)
Let p(z) be the second derivative of 0 + 13/42*z**3 + 1/7*z**2 + 76*z - 7/20*z**5 + 11/70*z**6 + 1/84*z**4. Determine w so that p(w) = 0.
-1/3, -2/11, 1
Factor -5/3*v**2 + v + 2/3.
-(v - 1)*(5*v + 2)/3
Let v(a) be the second derivative of a**5/60 + 5*a**4/18 - 7*a**3/2 - 108*a**2 - 11*a + 130. Find l such that v(l) = 0.
-9, 8
Suppose -m - 1 + 9 = 2*h, 4*h + 20 = 4*m. Let r be 16/m - ((-24)/18)/(-2). Factor w**4 - 6*w**2 + 4*w**2 + 4*w**2 - r*w**3 - w**3.
w**2*(w - 2)*(w - 1)
Let f be (0 + (-4)/(-9))*(-290 - -303). Determine c so that 2/9*c**2 - f*c + 338/9 = 0.
13
Solve 464*i**2 + 308*i**5 + 44*i - 12*i**3 - 175*i**5 - 117*i**5 + 112*i - 624*i**4 = 0 for i.
-1/2, 0, 1, 39
Let h(t) = -3*t**2 - 18*t + 2. Let u be h(-6). Let u*r**2 + 4 - r**2 - 6*r**2 + 25*r - 34 = 0. Calculate r.
2, 3
Let a(n) be the third derivative of -5*n**8/112 - 26*n**7/35 - 5*n**6/8 + 389*n**5/10 + 219*n**4 + 288*n**3 + 9*n**2 - 50. Find f such that a(f) = 0.
-8, -3, -2/5, 4
Let -13612*z + 13477*z - 4*z**3 + 165*z**2 - z**4 - 21*z**3 - 4*z**4 = 0. What is z?
-9, 0, 1, 3
Let u(m) be the third derivative of -m**5/12 - 175*m**4/24 + 130*m**3 - 1077*m**2. Suppose u(i) = 0. Calculate i.
-39, 4
Let y be (-18)/(-4)*(-10)/(-15). Let q = -15 - -18. Factor -3 + 2*r**y + 2*r - 2*r**3 + 2*r**2 - 2*r**q + 1.
-2*(r - 1)**2*(r + 1)
Let w = 246 + -244. Suppose -21*a**w + 18*a**2 - 15*a + 3 - 15 = 0. What is a?
-4, -1
Let t(l) be the first derivative of 2/9*l**4 + 27 + 2/45*l**5 + 32/3*l - 32/27*l**3 - 16/9*l**2. Factor t(c).
2*(c - 2)**2*(c + 2)*(c + 6)/9
Determine o, given that 249575*o**3 + 41935400*o - 11217275*o**2 - 40967660 + 8*o**5 - 21469*o**4 + 19544*o**4 - 3*o**5 = 0.
2, 127
Solve -96/5 + 14/5*i**4 + 88/5*i**3 - 32/5*i**2 - 352/5*i = 0.
-6, -2, -2/7, 2
Suppose 0 = -x + 362*a - 356*a + 4, -3*x - 2*a + 12 = 0. Let s(q) be the second derivative of 0 - 1/4*q**x - 33*q + 12*q**3 - 216*q**2. What is y in s(y) = 0?
12
Let x be 6 - 11/(55/(-120)). Factor 65 - x - 23 + d**2 - 7*d.
(d - 4)*(d - 3)
Let -183*t + 325*t + 317*t + 2*t**2 - 219 + 677 - t**2 = 0. Calculate t.
-458, -1
Let c be (-80)/(-38) - 54/513. Factor 5 + 0 - 548*l + 14850*l**2 - 1 + 3919*l**c.
(137*l - 2)**2
Let d(v) be the second derivative of -v**6/60 + 251*v**5/40 - 7209*v**4/8 + 229635*v**3/4 - 1062882*v**2 + 6693*v. Determine o so that d(o) = 0.
8, 81
Let a(r) = -10*r + 183. Let f be a(18). Factor 6*z - 485*z**4 - 12*z**2 + 494*z**4 + 6*z**f - 4*z**3 + 3 - 8*z**3.
3*(z - 1)**2*(z + 1)*(3*z + 1)
Suppose 3*u - 3 = 0, 0 = k + 4*k + 7*u - 5*u - 12. Let 0*r + 4/15*r**k + 0 - 2/15*r**4 - 2/15*r**3 = 0. Calculate r.
-2, 0, 1
Let w(d) = -2*d**3 - d - 1. Let n(m) = -5*m**3 + 195*m**2 - m - 197. Let t(a) = -5*n(a) + 10*w(a). Factor t(r).
