/277, 0
Let n(q) = -q + 6. Let z be ((-7)/(-21))/((-3)/(-18)). Let f be n(z). Suppose -k + 0*k - 5*k**2 + f*k**2 = 0. What is k?
-1, 0
Suppose -1/4*s**4 + 427/4*s**2 + 0 - 35*s**3 - 143/2*s = 0. Calculate s.
-143, 0, 1, 2
Factor -72/11 - 722/11*g**3 - 2660/11*g**2 + 894/11*g.
-2*(g + 4)*(19*g - 3)**2/11
Let o(g) be the second derivative of -g**7/1050 - g**6/120 + g**5/300 + g**4/24 - 12*g**2 + 43*g + 2. Let p(h) be the first derivative of o(h). Factor p(a).
-a*(a - 1)*(a + 1)*(a + 5)/5
Suppose -9*p - 60 = -10*p - 4*j, 0 = -4*p - 2*j + 100. Let -24*d + p*d**2 - 11/3*d**4 + 0 + 22/3*d**3 + 1/3*d**5 = 0. Calculate d.
-2, 0, 1, 6
Suppose 17*i + 1604 = -96. Let v = 316/3 + i. Factor -v*n + 4*n**2 + 0 + 10/3*n**3.
2*n*(n + 2)*(5*n - 4)/3
Let s be (1367/(-10) + 0)/((-7)/14). Let y = 275 - s. Find d, given that 8/5*d - 2/5*d**2 - y = 0.
2
Factor -p**5 - 36*p - 9*p + 536*p**4 + 72*p**2 - 66*p**3 + 56*p**3 - 552*p**4.
-p*(p - 1)**2*(p + 3)*(p + 15)
Factor -77/4 + 95/4*k + 1/4*k**3 - 19/4*k**2.
(k - 11)*(k - 7)*(k - 1)/4
Let t(h) be the second derivative of 24/5*h**2 + 53*h + 12/5*h**3 - 2 + 1/4*h**4. Solve t(n) = 0 for n.
-4, -4/5
Let y be (-22 + 20)*(-497)/710. Let 3/5*d**2 - y*d - 6/5 + 3/5*d**3 - 1/5*d**4 = 0. Calculate d.
-1, 2, 3
Let m = -10674 - -10678. Let a(k) be the second derivative of 0*k**m + 1/20*k**5 - 1/2*k**3 - 45*k + 0 - k**2. Factor a(d).
(d - 2)*(d + 1)**2
Let z(b) be the third derivative of -b**5/180 - 29*b**4/36 - 12*b**3 + 1826*b**2. Find k such that z(k) = 0.
-54, -4
Suppose 208 - 124/5*a + 2/5*a**2 = 0. Calculate a.
10, 52
Let k = 13/31 + 761/403. Let m = 356/143 - k. Factor -m*c**4 - 2/11*c**3 + 2/11*c + 0 + 2/11*c**2.
-2*c*(c - 1)*(c + 1)**2/11
Let h(t) = -4*t**2 - 3*t + 1. Let y(p) = -p**2 - p. Suppose 16 - 100 = 14*m. Let x(i) = m*h(i) + 26*y(i). Factor x(w).
-2*(w + 1)*(w + 3)
Let k(n) be the first derivative of -n**4 - 40*n**3 + 264*n**2 - 544*n - 1401. Find i such that k(i) = 0.
-34, 2
Suppose 3*x - 13 = -x - t, 0 = -x - 4*t + 7. Let n be (-1)/((-2)/(18/x)). Factor -40/3*j**n - 1/3 + 11/6*j + 4/3*j**2.
-(4*j - 1)**2*(5*j + 2)/6
Suppose 4*r = -4*k + 21 - 9, 0 = 2*k - 4*r - 12. Factor 3*y**k + 5*y**2 - 2*y + 11769*y**3 + 5*y - 11780*y**3.
y*(y - 3)*(y - 1)*(3*y + 1)
Let o = -10/10323 - -13774/10323. Solve 0*z - o + 4/3*z**2 = 0 for z.
-1, 1
Let l = 233 - 225. Suppose 6*n + 4*o = l*n, -3*n - 2*o = -16. Factor -1/5*v**2 + 0*v - 1/5*v**3 + 1/5*v**5 + 1/5*v**n + 0.
v**2*(v - 1)*(v + 1)**2/5
Let s(p) be the second derivative of p**7/5040 - p**6/720 - 3*p**4/4 - p**2/2 - 46*p. Let f(b) be the third derivative of s(b). Factor f(n).
n*(n - 2)/2
Let l(i) be the third derivative of -i**2 + 1/120*i**6 + 0 + 65/24*i**4 - 50/3*i**3 - 11*i - 7/30*i**5. Factor l(x).
(x - 5)**2*(x - 4)
Suppose -2*u + 4 = 4*n, -3*n = -0*u + 3*u - 6. Suppose 0 = u*m - 2*s - 14, 5*s - 5 + 4 = -4*m. Solve -4*v**2 + 7 + m*v - 7 = 0 for v.
0, 1
Let d(i) be the first derivative of 3*i + 27/4*i**4 + 103 - 243/20*i**5 - 27/2*i**2 + 77/4*i**3. Let d(j) = 0. What is j?
-1, 2/9, 1
Suppose -4*g + 2*m = -314, 7*m - 12*m = 2*g - 175. Factor -g*c**2 + 38*c**3 - 49 + 25 - 14*c**3 - 4*c**5 + 76*c + 8*c**4.
-4*(c - 2)*(c - 1)**3*(c + 3)
Let v = -49 - -46. Let s be v/15 - (-62)/10. What is j in -j**2 + j + 4*j + s*j**2 = 0?
-1, 0
Suppose 154*z + 174*z + 145 = -32*z + 865. Factor 2/9*c**z - 52/9*c - 6.
2*(c - 27)*(c + 1)/9
Let d(l) be the first derivative of 3*l**5/40 + 15*l**4/16 + 27*l**3/8 + 27*l**2/8 + 522. Solve d(q) = 0.
-6, -3, -1, 0
Suppose 3*h - 111 = 4*l, 0 = 2*l + 2*h - 7*h + 73. Let f be (-22)/l - 28/168. Suppose 0*x**3 - f*x**2 + 0*x + 3/4*x**4 + 0 = 0. Calculate x.
-1, 0, 1
Suppose 0 = -3*r + 4*q, 0 = r - 2*r - 2*q + 10. Suppose -3*s - 5*u - 25 = -r*s, 25 = 5*s - 5*u. Factor -5*g - 5*g**3 + 10*g**3 + 5*g**2 - 5*g**4 + s*g.
-5*g*(g - 1)**2*(g + 1)
Let u(o) = -o**3 + 23*o**2 + 49*o + 33. Let y be u(25). Factor 21*m - 2 + 4*m**2 - y - 22*m - 17*m.
2*(m - 5)*(2*m + 1)
Let c(b) be the second derivative of b**6/105 + 68*b**5/35 + 47*b**4/3 + 128*b**3/7 - 1179*b**2/7 + 2185*b + 3. Suppose c(d) = 0. What is d?
-131, -3, 1
Factor 95*i**2 - 305*i**2 - 488*i + 109*i**2 + 97*i**2.
-4*i*(i + 122)
Factor -258/7 + 2/7*r**2 - 256/7*r.
2*(r - 129)*(r + 1)/7
Let k(u) be the first derivative of -u**3 + 246*u**2 - 489*u - 350. Find c such that k(c) = 0.
1, 163
Let m = -1126 - -1386. Let s be 4 - (1 - -2 - 2). Suppose -60 + 76*g**3 + 131*g**2 + 15*g**4 + m*g + 14*g**s - 446*g**2 + 10*g**4 = 0. Calculate g.
-6, 2/5, 1
Suppose -z - 27 + 278 = 0. Let u = z - 59. Let 18 - 21*a**4 - u*a + 23 + 7 + 48*a**3 + 72*a**2 = 0. What is a?
-2, 2/7, 2
Solve -496/7 - 4/7*g + 4/7*g**3 + 496/7*g**2 = 0.
-124, -1, 1
Let s be 28/(-24)*2*(-20)/70. Let c(b) be the second derivative of 8/3*b**2 + 1/18*b**4 + 3 - s*b**3 - b. Find q, given that c(q) = 0.
2, 4
Let f be (-13160)/(-3500) - (-12)/50. Factor 27/7*z**3 + 0 + 3*z**2 + 3/7*z**5 + 15/7*z**f + 6/7*z.
3*z*(z + 1)**3*(z + 2)/7
Let m(c) be the first derivative of 2*c**3/21 + 708*c**2/7 - 1418*c/7 + 2016. What is s in m(s) = 0?
-709, 1
Let 32*x**3 - 3 - 8*x**2 + 2892*x - 5947*x - 90*x**2 + 2967*x + 27 + 18*x**4 = 0. Calculate x.
-3, -1, 2/9, 2
Let o be 2/3 - (-11)/((-198)/(-2436)). Let s = o + -2582/19. Factor -32/19 + 14/19*v**2 - 16/19*v - s*v**3.
-2*(v - 4)**2*(v + 1)/19
Let c be 12/(-36) - (-3 + 581/3). Let u = c - -193. Factor 4/3*v - 1/3*v**u - 4/3.
-(v - 2)**2/3
Let -2/11*q**4 + 17/11*q**2 + 17/11*q**3 - 68/11*q - 36/11 = 0. What is q?
-2, -1/2, 2, 9
Let g(h) = -h**3 + 18*h**2 - 15*h - 31. Let y be g(17). Let -3 - 15*i**2 + 45*i**4 - 40*i**4 + 5*i**y + 13 - 5*i = 0. Calculate i.
-2, -1, 1
Let n(x) be the first derivative of 2/7*x**2 - 70 + 16/7*x - 2/21*x**3. Suppose n(g) = 0. Calculate g.
-2, 4
Let o(m) = m**3 - 25*m**2 - 155*m + 1133. Let v be o(29). Factor -6/13*z**v - 190/13*z + 64/13.
-2*(z + 32)*(3*z - 1)/13
Let a = -607509 + 607512. Factor 32/7 - 2916/7*u**a - 648/7*u**2 + 144/7*u.
-4*(9*u - 2)*(9*u + 2)**2/7
Let x be (-6372)/(-135) - 12/10. Suppose 0 = 8*z + x - 70. Let 32/9*s**2 + 4/3*s**4 + 2/9*s**5 + 28/9*s**z + 2*s + 4/9 = 0. What is s?
-2, -1
Let y(u) be the second derivative of u**7/21 + 16*u**6/5 + 23*u**5/5 - 8*u**4 - 47*u**3/3 + 766*u. What is f in y(f) = 0?
-47, -1, 0, 1
Factor 98 + 50*h + 2*h**2 + 108 - 374.
2*(h - 3)*(h + 28)
Let i(p) be the second derivative of -p**6/135 - 2*p**5/45 - p**4/18 - 1411*p. Suppose i(u) = 0. What is u?
-3, -1, 0
Let y(m) = -m**4 - 67*m**3 + 137*m**2 + 71*m - 146. Let i(t) = 3*t**4 + 132*t**3 - 274*t**2 - 142*t + 296. Let u(s) = -4*i(s) - 10*y(s). Solve u(z) = 0.
-1, 1, 2, 69
Let c(n) be the second derivative of -n**5/20 + 25*n**4/12 + 53*n**3/6 + 27*n**2/2 + n + 667. Determine h so that c(h) = 0.
-1, 27
Suppose 2*q + 5*u - 30 = 0, 4*q - 5*u = 98 - 38. Factor 20*k - 50 - q*k - 19*k - 5*k**2 - 21*k.
-5*(k + 2)*(k + 5)
Let 188/7*q**2 - 4/7*q**3 - 52*q + 180/7 = 0. Calculate q.
1, 45
Let r(y) be the first derivative of -5*y**3/3 + 35*y**2 - 245*y + 309. Find g, given that r(g) = 0.
7
Let h = -258 - -261. Factor -39*c**2 + 60*c**3 + 76*c**4 + 9*c**h - 85*c**4 - 21*c.
-3*c*(c - 7)*(c - 1)*(3*c + 1)
Let v(u) = -u**3 - 1. Let g(k) = -6*k - 6*k**3 - 21*k**2 - 28*k**2 - 3 + 66*k**2 - 26*k**2. Let x(a) = -g(a) + 3*v(a). Factor x(o).
3*o*(o + 1)*(o + 2)
Let k be ((-32)/(-51))/(-4)*(-12)/16. Let o be (204/26 - 34/(-221))*3/6. Suppose 6/17*h**o + k*h**3 + 0 - 16/17*h**2 + 8/17*h = 0. What is h?
-2, 0, 2/3, 1
Let u(v) be the first derivative of -137 + 28/5*v**2 + 1/15*v**3 + 784/5*v. Factor u(t).
(t + 28)**2/5
Let r(d) = -2*d**2 + 20*d - 44. Suppose 5 + 19 = 6*a. Let w be r(a). Factor -1/3*n**w + 0*n + 0 - 1/3*n**2 - 2/3*n**3.
-n**2*(n + 1)**2/3
Let j be 3352560/488457 - 4/(-158). Factor j*o**2 - 2/9*o**3 - 448/9*o - 512/9.
-2*(o - 16)**2*(o + 1)/9
Suppose 200807815 = 794*z - 38449217 + 48697032. Suppose -120*k**3 - 48000*k + 3/2*k**4 + 3600*k**2 + z = 0. What is k?
20
Let k(i) be the first derivative of -i**6/90 + 11*i**5/30 + 2*i**4 + 62*i**3/3 - 70. Let r(o) be the third derivative of k(o). Factor r(n).
-4*(n - 12)*(n + 1)
Let y(p) = -p**3 - 10*p**2 + 81*p - 26. Let z be y(5). Let k(t) be the first derivative of 7/4*t**z + 0*t + 6 - 5*t**3 + 9/2*t**2 - 1/5*t**5. Factor k(j).
-j*(j - 3)**2*(j - 1)
Let -109*r