, 0, 1
Let h = -591/19129 + 2/517. Let k = 139/333 - h. Suppose 2/9*d**3 + 0*d**2 - 2/3*d - k = 0. Calculate d.
-1, 2
Suppose -18 = -5*s + j, 3*j + 11 = 2. Suppose 11 = 4*f - s*m + 4*m, 3*m - 11 = -f. Factor 18/7*p**f - 8/7*p**3 + 2/7 - 12/7*p.
-2*(p - 1)**2*(4*p - 1)/7
Let c = 823 + -3291/4. Let k(d) be the first derivative of 0*d - 1/12*d**3 + c*d**2 - 3. Suppose k(s) = 0. Calculate s.
0, 2
Find k, given that 20/13*k**4 + 2/13*k**5 + 8*k + 74/13*k**3 + 128/13*k**2 + 32/13 = 0.
-4, -2, -1
Let k(c) = c**3 + c. Let l be (-1)/((3/3)/(-1)). Let g be k(l). Factor -h**4 - 1 + h**3 + g*h + 2*h**4 - 3*h**3.
(h - 1)**3*(h + 1)
Let d be -6*51/((-8721)/38). Factor -1/3*c**2 - 4/3*c**3 + 1/3*c**4 + d*c + 0.
c*(c - 4)*(c - 1)*(c + 1)/3
Let a(t) = -3*t**2 - t. Let b(q) = -22*q**2 - 138*q - 128. Let l(m) = -6*a(m) + b(m). Let l(v) = 0. Calculate v.
-32, -1
Let y be (-1)/77*-413 - 5. Factor 0 + y*g**3 + 0*g + 2/11*g**4 + 0*g**2 - 2/11*g**5.
-2*g**3*(g - 2)*(g + 1)/11
Let a(n) = n**3 - 17*n**2 + 5*n - 4. Let f be a(8). Let b be f/(-70) + 2/7. Find u, given that -4*u**2 + 2 - 12*u**2 + u - 7*u - b*u = 0.
-1, 1/8
Suppose -5*h = -4*r - 16, -3*r - 7 = -3*h + 2*r. Suppose 14*m - 36 = -h*m. Let -4/13 - 2/13*k**3 - 8/13*k**m - 10/13*k = 0. Calculate k.
-2, -1
Let i(y) be the second derivative of -y**6/120 + 9*y**5/16 - 225*y**4/16 + 1125*y**3/8 + 2*y - 5. Factor i(l).
-l*(l - 15)**3/4
Let k(f) be the second derivative of -2/21*f**4 - 2/21*f**3 - 1/35*f**5 + 0*f**2 + 12*f + 0. Determine l so that k(l) = 0.
-1, 0
Let n(m) be the second derivative of -1/48*m**4 + 2*m + 0*m**2 - 5 + 0*m**3 + 1/80*m**5. Factor n(l).
l**2*(l - 1)/4
Let h(i) be the second derivative of i**7/189 + 2*i**6/27 + 4*i**5/15 + 11*i**4/27 + 7*i**3/27 - 3*i + 5. Let h(y) = 0. What is y?
-7, -1, 0
Let p be ((-52)/(-286))/((-1)/(-4)). Factor -p + 10/11*c - 2/11*c**2.
-2*(c - 4)*(c - 1)/11
Let z = 22 + -17. Suppose -3*v + 5 = p, 0*v - p + 9 = z*v. Find x, given that -5*x**2 - x**2 + 3*x**v - 1 - 2 + 6*x = 0.
1
Let n be 1/(((-22)/(-4))/11). Let -468*w + 5*w**2 + 418*w + 0*w**n = 0. Calculate w.
0, 10
Let n(r) be the second derivative of 2*r**6/15 - 4*r**5/5 - 5*r**4/3 + 143*r. Factor n(x).
4*x**2*(x - 5)*(x + 1)
Let o be (-16 + 2)*20/(-8). Let -2*w**5 + 37*w**3 - o*w**3 - 5*w + 5*w = 0. What is w?
-1, 0, 1
Let f(k) be the first derivative of -k**5/45 + k**4/36 + 2*k**3/9 + 63. Factor f(o).
-o**2*(o - 3)*(o + 2)/9
Suppose 5*k - l = 19, -17 = 5*k - 8*k - 5*l. Suppose 0 = -4*s + s + 42. Determine f so that -2*f**2 + s - 14 + k*f = 0.
0, 2
Let n = -49 + 54. Factor -8*f**4 - 2*f**n + 2*f**3 - 2*f**4 - 16*f**3 - 6*f**2.
-2*f**2*(f + 1)**2*(f + 3)
Let u(s) be the second derivative of -1/4*s**2 - 5/12*s**4 - 1/84*s**7 - 1/4*s**5 - 8*s - 1/12*s**6 - 5/12*s**3 + 0. Determine o so that u(o) = 0.
-1
Let h(y) = -2*y**4 - 21*y**3 - 42*y**2 - 41*y. Let m(o) = o**3 + o. Let c(w) = -h(w) - 5*m(w). Find j such that c(j) = 0.
-3, -2, 0
Let m be (2 - (3 + -11)) + 17 + -24. Factor 12/11*o + 24/11*o**2 + 6/11*o**4 + 2/11 + 20/11*o**m.
2*(o + 1)**3*(3*o + 1)/11
Find v, given that -4/9*v + 70/9*v**2 - 44/3*v**4 - 58/9*v**3 + 0 = 0.
-1, 0, 2/33, 1/2
Find l such that -42/5*l**3 + 0 - 16/5*l**4 - 2/5*l**5 + 0*l - 36/5*l**2 = 0.
-3, -2, 0
Let b(k) be the first derivative of 98*k - 14*k**2 + 2/3*k**3 - 31. Find m, given that b(m) = 0.
7
Let v(f) = -2*f**2 + 23*f + 18. Let d be v(12). Suppose -7*m + 15 = -d. Find b, given that 16*b**2 + 16/3*b**4 - 2/3*b**5 + 0 - 44/3*b**m - 6*b = 0.
0, 1, 3
What is d in 0*d - 3/2*d**4 + 0 + 3/2*d**3 + 3*d**2 = 0?
-1, 0, 2
Let f(d) = -d**2 + 2*d - 2*d - 98 + 99. Let s(w) = 3*w**2 + 6*w + 7. Let l(y) = 2*f(y) + s(y). Factor l(x).
(x + 3)**2
Let p be (-138)/(-33) - (-6)/(-33). Let 3 - 149*n**3 - 3*n**5 + 119*n**3 - n**p + 30*n**2 + 16*n**4 - 15*n = 0. What is n?
1
Suppose 2601/4 - 51/2*o + 1/4*o**2 = 0. What is o?
51
Let o(r) be the first derivative of 27*r**4/8 - 5*r**3/8 - 167. Solve o(h) = 0.
0, 5/36
Let w(l) be the third derivative of l**9/5040 + l**8/960 - l**6/180 + 5*l**4/24 - 5*l**2. Let q(t) be the second derivative of w(t). Factor q(s).
s*(s + 1)*(s + 2)*(3*s - 2)
Let y(q) = 4 + 7 + 6*q + 0 + q**2. Let l(f) = 3*f**2 + 18*f + 32. Let g(k) = -3*l(k) + 8*y(k). Factor g(i).
-(i + 2)*(i + 4)
Determine h, given that 1196/7*h**3 + 4000000/7 - 4/7*h**4 + 3880000/7*h - 118800/7*h**2 = 0.
-1, 100
Suppose -3*t - 4*l + 27 = 0, 5*t + l - 29 = -1. Solve s**4 + 4*s**3 + 0*s**4 - t*s**4 + 32*s**2 - 48*s = 0 for s.
-3, 0, 2
Suppose -3*d + 5*f + 73 = 0, f = -d + 3*f + 25. Let l be 72/21 + 12/d. Factor 2*o**2 + 0 + 4/5*o**l - 11/5*o**3 - 3/5*o.
o*(o - 1)**2*(4*o - 3)/5
Let g be ((-70952)/231)/(2/(-6)). Let l = g - 920. Factor 0*x + 0 + l*x**3 + 8/11*x**2 - 10/11*x**4.
-2*x**2*(x - 2)*(5*x + 2)/11
Suppose 7*s + 56 - 14 = 0. Let f(y) = -3*y**4 + 6*y**3 - 15*y**2 - 6*y. Let t(g) = -5*g**4 + 11*g**3 - 29*g**2 - 12*g. Let z(u) = s*t(u) + 11*f(u). Factor z(l).
-3*l*(l - 2)*(l + 1)**2
Suppose -4*g + 15 = x, 5*g - 30 = -6*x + 7*x. Let h(d) be the first derivative of 3*d + d**2 - 1/3*d**3 + g. Factor h(n).
-(n - 3)*(n + 1)
Factor 10*g - 5*g**2 + 40/3 - 5/3*g**3.
-5*(g - 2)*(g + 1)*(g + 4)/3
Let b(j) = j**2 - 2*j + 3. Let s be b(2). Suppose -3*t - t = s*i - 35, i = t. Factor 7*g - g + g - t*g + 2*g**2.
2*g*(g + 1)
Let c(z) = -10*z**4 - 10*z**3 + 25*z**2 - 35*z + 15. Let v(f) = -9*f**4 - 8*f**3 + 26*f**2 - 36*f + 15. Let x(s) = -4*c(s) + 5*v(s). Factor x(r).
-5*(r - 1)**3*(r + 3)
Let z be (8/6)/(16/24). Factor -8*c**3 + 2*c**4 + 81*c**2 - 165*c**2 - 4*c + 94*c**z.
2*c*(c - 2)*(c - 1)**2
Factor -242/7*t + 1/7*t**2 + 241/7.
(t - 241)*(t - 1)/7
Let z(i) be the first derivative of 0*i + 5/12*i**6 + 0*i**2 - 3/2*i**5 + 0*i**3 - 19 + 5/4*i**4. Suppose z(n) = 0. What is n?
0, 1, 2
Let g = -1765/2 - -884. Let l(s) be the first derivative of -5 + 0*s**3 - 3/16*s**4 + g*s + 9/8*s**2. Solve l(h) = 0 for h.
-1, 2
Let r(c) = c**2 - 15*c + 18. Let n be r(15). Factor 13*p**3 - 18 + n - 25*p**2 - 10*p - 33*p**3 - 5*p**4.
-5*p*(p + 1)**2*(p + 2)
Find l, given that 1/2*l**2 + 0*l + 0 - l**3 + 1/2*l**4 = 0.
0, 1
Let b(l) be the first derivative of l**6/30 - 2*l**5/15 - l**4/6 + 4*l**3/3 + 11*l**2 + 3. Let g(t) be the second derivative of b(t). Factor g(v).
4*(v - 2)*(v - 1)*(v + 1)
Let h be ((-4)/(-11))/((-546)/(-1001)). Let p(c) be the second derivative of -h*c**3 + 0*c**2 + 0 + 1/6*c**4 - 7*c. Factor p(z).
2*z*(z - 2)
Factor -2/7*c + 0 + 1/7*c**4 - 1/7*c**2 + 2/7*c**3.
c*(c - 1)*(c + 1)*(c + 2)/7
Let h(l) be the first derivative of 0*l + 5 - 3/40*l**5 + 3/32*l**4 + 1/4*l**3 + 0*l**2. Find j such that h(j) = 0.
-1, 0, 2
Let q(y) = -y**3 + 2*y**2. Let l(h) = 5*h**4 - 63*h**3 - 9*h**2 + 65*h. Let z(c) = l(c) + 2*q(c). What is v in z(v) = 0?
-1, 0, 1, 13
Factor -6*m**4 + 0*m - 8/3*m**3 + 5/3*m**5 + 0*m**2 + 0.
m**3*(m - 4)*(5*m + 2)/3
Let c = -3940 - -3940. Factor 4/5*y**2 - 16/5 + c*y.
4*(y - 2)*(y + 2)/5
Let j be (6/88)/((-29)/(3016/(-39))). Factor -8/11 + j*n**2 - 6/11*n.
2*(n - 4)*(n + 1)/11
Suppose -2*y + 4*n + 36 = -20, n + 25 = y. Factor 3*c**3 - 49*c - 6*c**2 + c - 12 + 5*c + y*c.
3*(c - 4)*(c + 1)**2
Let v(o) be the first derivative of -o**7/4200 - o**6/450 - o**5/120 - o**4/60 + o**3/3 + 10. Let x(q) be the third derivative of v(q). Factor x(h).
-(h + 1)**2*(h + 2)/5
Let j(d) = -d**2 - 11*d - 5. Let m be j(-11). Let c(g) = -g - 1. Let y be c(m). Factor 8*k**3 + 0*k**3 - 6*k**3 - k**y.
-k**3*(k - 2)
Let x = 223 - 218. Let h(z) be the first derivative of 2/5*z**x + 0*z**3 + 0*z**2 + 0*z - 1/6*z**6 + 6 + 0*z**4. Factor h(c).
-c**4*(c - 2)
Suppose 0 = -4*k - 5 + 17. Suppose 0 = 3*y + 15, -2 = -k*m - y - 1. Solve -c**4 + 0*c + 0*c**m + 0 - 1/3*c**5 - 2/3*c**3 = 0 for c.
-2, -1, 0
Let x = 226/147 - -88/49. Factor 1/3*j**2 + x*j + 25/3.
(j + 5)**2/3
Let u(y) be the first derivative of -y**6/120 - y**5/40 + y**3/12 + y**2/8 - 8*y + 19. Let w(t) be the first derivative of u(t). Factor w(b).
-(b - 1)*(b + 1)**3/4
Let r = 360 - 2159/6. Factor 0 - 1/6*i**3 + r*i - 1/6*i**2 + 1/6*i**4.
i*(i - 1)**2*(i + 1)/6
Suppose -72 + 1/4*b**2 - 71/2*b = 0. What is b?
-2, 144
Let 2/7*v**3 + 0 + 2/7*v - 4/7*v**2 = 0. Calculate v.
0, 1
Let c(y) be the third derivative of -y**6/30 - 3*y**5/5 - y**4 + 32*y**3/3 + 27*y**2. What is j in c(j) = 0?
-8, -2, 1
