 0. Factor -3/2*k + n + 1/2*k**2.
(k - 2)*(k - 1)/2
Let b(r) be the first derivative of -r**4/18 + 62*r**3/27 - 112*r**2/9 + 24*r - 2440. Let b(i) = 0. Calculate i.
2, 27
Let j = -102 - -111. Let q(n) = 9*n**3 + 6*n**2 - 36*n - 24. Let o(u) = -18*u**3 - 12*u**2 + 72*u + 48. Let v(k) = j*q(k) + 4*o(k). Factor v(g).
3*(g - 2)*(g + 2)*(3*g + 2)
Suppose 2 = 25*h - 23. Let p be h + -2 + (-14)/((-42)/9). Factor 1/3*y + 0 + 1/6*y**p.
y*(y + 2)/6
Let y(n) be the third derivative of n**5/60 + 23*n**4/3 + 182*n**3/3 - 756*n**2. Factor y(h).
(h + 2)*(h + 182)
Let p(o) be the first derivative of -63*o**5/25 - 12*o**4/5 + 4*o**3/3 + 8*o**2/5 - 2915. Factor p(b).
-b*(3*b + 2)**2*(7*b - 4)/5
Let s(p) = 3*p**5 + 6*p**4 + p**2 - 1. Let g(j) = -j**5 - 48*j**4 + 40*j**3 + 1407*j**2 + 3648*j + 2721. Let q(r) = g(r) + s(r). Factor q(y).
2*(y - 17)*(y - 10)*(y + 2)**3
Suppose 2*u + 5*w + 5 = -2*u, u - 2*w = 2. Let l be ((-21)/6)/(-7)*u - -2. Factor -22*b - 8*b + 125 - 2*b**l - 20*b + 7*b**2.
5*(b - 5)**2
Suppose 7*v - 752 + 738 = 0. Let p = -7 - -9. Find d such that -2*d**2 + 7*d**2 - 4*d**2 + d**p - v = 0.
-1, 1
Let u(h) be the first derivative of 1/8*h**4 - 2/3*h**3 - 3*h + 75 - 11/4*h**2. Solve u(z) = 0 for z.
-1, 6
Determine s, given that 4*s**4 + 9*s - 514824 - 9*s**3 + 3*s**2 - s**4 + 514818 = 0.
-1, 1, 2
Solve -8 - 6*j**3 - 7*j**3 + 18*j**2 + 16*j - 2*j**5 - 40*j**2 - j**3 + 20*j**2 + 10*j**4 = 0 for j.
-1, 1, 2
Let o = 3005/249 - -149/249. Determine k, given that -361/3 - 1/3*k**2 - o*k = 0.
-19
Let h(k) be the second derivative of -k**4/12 - 79*k**3/6 - 39*k**2 - 2*k - 208. Factor h(j).
-(j + 1)*(j + 78)
Suppose -2*s + 1026 = -4*w, -s + 5*s - 2030 = -3*w. Let c = 509 - s. Solve -8/15*x**4 + 2/5*x**5 - 2/15*x - 4/15*x**3 + 8/15*x**2 + c = 0 for x.
-1, 0, 1/3, 1
Solve -720/7*y - 717/7 - 3/7*y**2 = 0 for y.
-239, -1
Suppose -69 + 216 + 207 = -34*n + 152*n. Suppose 6*l - l = 0. Suppose -2/3*j**2 + l - 1/3*j**n - 1/3*j = 0. What is j?
-1, 0
Let b(y) = 9*y + 97. Let t be b(-10). Suppose 2 - 5*a**4 + 2 + 4*a + t*a**2 + 7*a**2 - 5 - 8 - 4*a**3 = 0. Calculate a.
-9/5, -1, 1
Let k(y) be the second derivative of 5*y**4/36 + 5270*y**3/9 + 2777290*y**2/3 + 208*y - 7. What is s in k(s) = 0?
-1054
Let u(n) be the second derivative of n**5/10 - 6*n**4 - 415*n**3/3 + 450*n**2 + 25*n + 11. Factor u(v).
2*(v - 45)*(v - 1)*(v + 10)
Let f(x) be the third derivative of -1/72*x**4 - 24 + 0*x**3 - 1/1260*x**7 + 1/120*x**5 + 3*x**2 + 0*x + 0*x**6. What is b in f(b) = 0?
-2, 0, 1
Let d be (-6)/(-15) + ((-23)/(-5) - 1). Suppose -5*o - 3*u + 423 = -d*u, 0 = -2*u + 4. Suppose -165*t**2 + t + 9*t + o*t**2 + 85*t**2 + 5 = 0. What is t?
-1
Let f(p) be the second derivative of -2/3*p**3 + 0 - 1/8*p**4 + 4*p + 1/60*p**5 + 5*p**2. Let v(c) be the first derivative of f(c). Factor v(k).
(k - 4)*(k + 1)
Let n(m) = m**3 - 5*m**2 - 32. Let y be n(6). Let z be (8/y - -3) + (-9)/3. Factor -2*q - 1009*q**5 - 10*q**2 - 6*q + z*q**2 + 6*q**3 + 1007*q**5 + 4*q**4.
-2*q*(q - 2)**2*(q + 1)**2
Let x(y) be the second derivative of 3*y**6/70 - 3*y**5/5 + 73*y**4/28 - 24*y**3/7 + y + 105. Suppose x(k) = 0. Calculate k.
0, 1, 3, 16/3
Let w(k) be the third derivative of -k**7/105 - k**6/20 + k**5/5 + 7*k**4/3 + 8*k**3 + 2*k**2 + 220. Factor w(r).
-2*(r - 3)*(r + 2)**3
Let a be ((-1065)/75 - -19)/((-3)/(-10)). Let c(m) be the first derivative of -64*m + 34 - a*m**2 - 4/3*m**3. Suppose c(r) = 0. Calculate r.
-4
Let r(z) be the first derivative of -2*z**5/35 + 41*z**4/14 - 318*z**3/7 + 1159*z**2/7 - 1444*z/7 - 40. Find o such that r(o) = 0.
1, 2, 19
Let k(d) be the third derivative of d**5/510 - d**4/51 - 5*d**3/51 - 614*d**2. Determine n, given that k(n) = 0.
-1, 5
Let c(j) be the first derivative of 3*j**5/35 + 3*j**4/28 - 2*j**3/7 + 6599. Factor c(p).
3*p**2*(p - 1)*(p + 2)/7
Let l = 40 + -24. Let u = l + -3. Let 6*v**4 + u*v**2 - 4*v**3 - 18*v**4 + 4*v - v**2 = 0. Calculate v.
-1, -1/3, 0, 1
Let i be (4374/180)/((1 - 16/40)*1/1). Solve 135*w**2 + 3/2*w**5 + 33/2*w**4 + i + 69*w**3 + 243/2*w = 0 for w.
-3, -1
Let b(x) = 2*x**2 - 2*x. Let z be b(-1). Factor 103 - 4*h**3 - 4*h**2 - 52 + z*h**4 + 4*h - 51.
4*h*(h - 1)**2*(h + 1)
Let z = 616 + -616. Factor 31*h**2 + z*h**3 + 4*h**3 + 30*h + 19*h**2 + h**3 + 15*h.
5*h*(h + 1)*(h + 9)
Let g be ((13254/(-20))/((-24)/(-32)))/(4 + (-81)/18). Factor -188/5*j - g - 1/5*j**2.
-(j + 94)**2/5
Let o be (-7)/(35/(-100))*(41/(-492))/((-28)/40). Let -2/21*u**3 - 176/21*u - 8 - o*u**2 = 0. What is u?
-21, -2
Suppose -133*n + 314 = -351. Let u(j) be the third derivative of 0 - 1/180*j**6 + 0*j**3 + 0*j + 1/9*j**4 + 0*j**n - 26*j**2. Factor u(b).
-2*b*(b - 2)*(b + 2)/3
Let g(p) be the third derivative of p**5/60 - 61*p**4 + 89304*p**3 + 2*p**2 - 241*p. Determine s so that g(s) = 0.
732
Suppose 102 = 3*a - 3*k, 4*a - 2*k - 132 = -0*k. Factor a*v - 6882 - 3*v**2 + 46*v + 4759 - 5989 + 234*v.
-3*(v - 52)**2
Factor -153/7 + 93/7*w + 3/7*w**3 + 57/7*w**2.
3*(w - 1)*(w + 3)*(w + 17)/7
Let j(p) = 104*p**2 - 72 - 113*p + 105*p**2 - 244*p**2 - 9*p**3. Let m(n) = -4*n**3 - 18*n**2 - 56*n - 36. Let b(q) = 2*j(q) - 5*m(q). Factor b(y).
2*(y + 1)*(y + 3)*(y + 6)
Suppose 2*x - 32 = -4*g, -3*x - 3*g + 18 = -7*g. Suppose -59 = -2*d - 5*j, -5*j = 5*d - x*j - 60. Solve -y**2 + d*y**4 - 13*y**4 - y**3 + 4*y**3 = 0.
-1, 0, 1/4
Let s = 81116 - 567802/7. Factor -s + 12/7*i - 2/7*i**2.
-2*(i - 5)*(i - 1)/7
Let u(s) be the second derivative of 15*s**3 - 21/40*s**5 + 12*s**2 - 2*s + 3/2*s**4 - 12. Find y such that u(y) = 0.
-2, -2/7, 4
Let r be 63/6*(-764)/(-5348). Solve -r*s - 3/4*s**2 + 45/4 = 0 for s.
-5, 3
Let r(o) be the second derivative of 4*o**7/147 - 37*o**6/105 + 121*o**5/70 - 86*o**4/21 + 100*o**3/21 - 16*o**2/7 - 2*o + 85. Solve r(a) = 0.
1/4, 1, 2, 4
Let j(u) be the second derivative of -u**5/30 + 46*u**4/27 + 229*u**3/27 + 22*u**2/3 - 4296*u - 2. Find m such that j(m) = 0.
-2, -1/3, 33
Let b = -5637/4060 - -121/87. Let l(t) be the third derivative of -1/70*t**5 - b*t**6 + 4/21*t**3 + 0*t + 13*t**2 + 0 + 0*t**4. Suppose l(f) = 0. Calculate f.
-2, 1
Suppose -37*r + 35*r - 82 = 0. Let p = -39 - r. Let 24*h**2 - 12*h**3 + 12*h**5 - 32*h**2 + p*h**4 + 6*h**4 = 0. Calculate h.
-1, -2/3, 0, 1
Let x be 0 + (4 - (-702)/(-189)). Suppose -4/7*i - 2/7*i**4 - 6/7*i**3 + 0 + 10/7*i**2 + x*i**5 = 0. Calculate i.
-2, 0, 1
Let r(g) be the first derivative of 1/9*g**6 + 5/6*g**4 + 8/15*g**5 + 3 + 4/9*g**3 + 0*g**2 + 0*g. Factor r(l).
2*l**2*(l + 1)**2*(l + 2)/3
Let q(y) be the third derivative of 55/6*y**4 + 0*y + 121/12*y**5 + 10/3*y**3 - 18 + 7*y**2. Solve q(g) = 0 for g.
-2/11
Solve 121*a**4 - 50*a**4 - 8*a**4 + 63*a**5 + 1 - 108*a + 120*a**4 - 195*a**2 + 45*a**3 + 11 = 0.
-2, -1, 2/21, 1
Let l(m) = -4*m**2 + 708*m - 2118. Let y(u) = 33*u**2 - 5662*u + 16944. Let s(v) = -17*l(v) - 2*y(v). Factor s(r).
2*(r - 353)*(r - 3)
Let u(p) be the second derivative of p**4/6 - 3896*p**3/3 + 3794704*p**2 + 310*p. Suppose u(g) = 0. What is g?
1948
Let b = 274654 - 1922575/7. Suppose 1/7*w**5 + 1/7*w**4 + 0 + 2/7*w - 1/7*w**2 - b*w**3 = 0. Calculate w.
-2, -1, 0, 1
Factor -61/5*b + 66 - 1/5*b**2.
-(b - 5)*(b + 66)/5
Determine t, given that -3*t**2 - 3/5*t**3 + 48 + 102/5*t = 0.
-8, -2, 5
Let y be (-52*12/126)/(50/(-75)). Determine p so that 128/7 + 2/7*p**5 + 8/7*p**2 - 10/7*p**4 - y*p**3 + 176/7*p = 0.
-2, -1, 2, 8
Let y be ((-171)/19 + 5)*3*5/(-20). Factor 14/3*q**2 - 2*q**y - 2/9*q**4 + 0 - 22/9*q.
-2*q*(q - 1)**2*(q + 11)/9
Let a(v) be the second derivative of 121*v**7/42 + 33*v**6/5 - 5*v**5 - 2*v**4 - v + 94. Find l such that a(l) = 0.
-2, -2/11, 0, 6/11
Let t be 18 + (-7 - -8) - 7. Factor 0 - t*m**2 - 2/5*m**3 + 0*m.
-2*m**2*(m + 30)/5
Let r be -10 + 16 - (13 + -11) - 1. Let n(w) = -w**3 + w**2 + 5*w + 3. Let a be n(-2). Solve 0 + 4/9*q**4 - 5/9*q**r + 0*q - 1/9*q**a + 2/9*q**2 = 0 for q.
0, 1, 2
Factor -14*z**3 - 30*z**2 - 3266*z**4 + 3*z**5 + 3278*z**4 - 16*z**3 + 9*z**3.
3*z**2*(z - 2)*(z + 1)*(z + 5)
Find f, given that -4*f**3 - 240 + 1716*f + 2*f**3 + 34*f**2 - 1760*f = 0.
-2, 4, 15
Let 52 + 20/3*b**2 + 103/3*b + 1/3*b**3 = 0. Calculate b.
-13, -4, -3
Let g(k) = -216*k + 36506. Let c be g(169). What is m in 0 - 4/3*m - c*m**4 + 2*m**2 + 2/3*m**5 + 2/3*m**3 = 0?
-1, 0, 1, 2
Factor -132*i - 5*i**5 + 126*