/3*t**3 - s*t**2 + 8/3*t + 31/3*t**4 = 0. What is t?
-1, -2/7, 2/5, 1
Let c = -25 - -54. Let n = 32 - c. Factor 5*a**3 - 11*a**n - 8*a**2 + 2*a**3 + 4*a**5 + 8*a**4.
4*a**2*(a - 1)*(a + 1)*(a + 2)
Suppose 5*w - 10 = -0*w. Let r = 9837/2863 + -3/409. Factor -60/7*g**4 + 8/7*g + 50/7*g**5 + r*g**w - 22/7*g**3 + 0.
2*g*(g - 1)**2*(5*g + 2)**2/7
Factor 16/7*o + 8/7*o**2 - 16/7*o**3 - 1/7*o**5 + o**4 - 16/7.
-(o - 2)**4*(o + 1)/7
Let c be (-30)/9*12/(-10). Suppose n = -c*n. Suppose 3*p**2 - 3*p**3 + 0*p**2 + 0*p**3 + n*p**2 = 0. What is p?
0, 1
Suppose -6 = -3*j - 3*k, 20*j + 10 = 25*j - 2*k. Let p(g) be the second derivative of 0*g**j + 1/42*g**4 - 6*g + 0 - 1/21*g**3. Factor p(n).
2*n*(n - 1)/7
Let c(l) be the first derivative of -1/4*l**4 + 7/3*l**3 + 0*l - 3*l**2 - 13. Determine y, given that c(y) = 0.
0, 1, 6
Let k(q) be the first derivative of q**8/420 - q**6/30 + q**5/15 - 32*q**3/3 + 45. Let v(d) be the third derivative of k(d). Factor v(g).
4*g*(g - 1)**2*(g + 2)
Let o(y) = -17*y**5 + 12*y**4 - y**2 - 5*y. Let a(z) = 9*z**5 - 6*z**4 + 3*z. Let g = 53 + -64. Let r(c) = g*a(c) - 6*o(c). Factor r(b).
3*b*(b - 1)**3*(b + 1)
Suppose -24 = 4*i + 5*b - 17, 0 = 4*i + 4*b + 4. Let a(w) be the first derivative of 2/5*w**i - 6/5*w + 2/15*w**3 + 7. Find n such that a(n) = 0.
-3, 1
Let h(q) be the first derivative of q**3 - 27*q**2/2 + 46. Factor h(j).
3*j*(j - 9)
Let h(i) be the second derivative of -i**4/28 - 71*i**3/42 - 23*i**2/7 + 340*i. Solve h(j) = 0.
-23, -2/3
Let i(j) = j**5 - 19*j**3 + 18*j**2 + 4*j + 4. Let z(v) = 5*v**5 - 115*v**3 + 110*v**2 + 25*v + 25. Let u(h) = 25*i(h) - 4*z(h). Let u(b) = 0. What is b?
-2, 0, 1
Suppose 4*l = y + 3*y - 4, 2*y = 3*l - 3. Let t(g) be the first derivative of -4/9*g + 1/3*g**2 + 1/6*g**4 + y + 16/27*g**3. Factor t(u).
2*(u + 1)*(u + 2)*(3*u - 1)/9
Let o(v) = 13*v**4 - 16*v**3 + 19*v**2 + 4. Let h(u) = 11*u**4 - 17*u**3 + 18*u**2 + 3. Let f(k) = -4*h(k) + 3*o(k). Find j such that f(j) = 0.
0, 1, 3
Let y be 170/15 + 2/3. Suppose 5*j - 2*q - y = 0, -j + q + 12 = 3*j. Factor j + 2*u**3 + 1 - 2*u - 3 - 4*u**2 + 2.
2*(u - 2)*(u - 1)*(u + 1)
Let t(f) = 36*f**4 + 110*f**3 - 19*f**2 - 109*f - 15. Let c(x) = -x**4 - x**2 - x. Let p(i) = -c(i) - t(i). Solve p(v) = 0 for v.
-3, -1, -1/7, 1
Let g = -1447364/12245 + 1/2449. Let p = 119 + g. Factor 6/5*c**3 - p*c**2 - 2/5*c**4 + 0 + 0*c.
-2*c**2*(c - 2)*(c - 1)/5
Let g(r) be the second derivative of -15*r**7/7 - 35*r**6/2 - 31*r**5/2 + 135*r**4/4 + 70*r**3 + 50*r**2 + 14*r. Solve g(d) = 0.
-5, -2/3, -1/2, 1
Let n = 77 - 75. Solve 21*f**3 + 12*f**3 + 129*f - 24 + 126*f**n - 21*f = 0.
-2, 2/11
Suppose -3*j = j + 8. Let u be (1*1/j)/(2/(-12)). Suppose 27*s**4 - 36*s**u - 27/4*s**5 - 21/4*s + 1/2 + 41/2*s**2 = 0. Calculate s.
1/3, 1, 2
Let s = -11733/2 + 5868. Factor -s*j**2 + 9/2*j - 3.
-3*(j - 2)*(j - 1)/2
Suppose 3*i + 0*i = -b, -5*i + b = -0*b. Suppose 3/2 - 3/2*f**2 + i*f = 0. What is f?
-1, 1
Let 6 - 6*c + 3/2*c**2 = 0. Calculate c.
2
Let a = 32 + -68. Let r be (a/150)/(4*3/(-30)). Suppose -r*s**2 + 0 - 3/5*s**3 + 0*s = 0. What is s?
-1, 0
Let x(i) be the second derivative of i**7/5040 - i**6/480 - i**5/60 + 5*i**4/12 - 14*i. Let m(z) be the third derivative of x(z). Let m(g) = 0. Calculate g.
-1, 4
Let t(g) be the third derivative of g**5/60 - 7*g**4/8 - 78*g**2. Suppose t(d) = 0. What is d?
0, 21
Factor 350 + 8/7*w**2 + 40*w.
2*(2*w + 35)**2/7
Let v = 126 - 110. Suppose 0*d - v = -5*z + 2*d, -3*z + 4*d = -18. Let -n**3 + 9/4*n - 1/2 - 3/4*n**z = 0. Calculate n.
-2, 1/4, 1
Determine n so that -195/4*n**3 + 3/4*n**4 + 0*n**2 + 0 + 0*n = 0.
0, 65
Let b be -2 - -6*(1 - (-48)/(-81)). Let s be (-14)/(-105) + 68/90. Factor b*n**3 - s*n**2 + 0*n + 0.
4*n**2*(n - 2)/9
Let m(x) = x**2 - 13*x - 3262. Let z be m(-51). Factor 162/11 + 36/11*c + 2/11*c**z.
2*(c + 9)**2/11
Let t(v) be the second derivative of v**5/70 + v**4/42 - 8*v**3/21 - 12*v**2/7 + 90*v. Determine w, given that t(w) = 0.
-2, 3
Let p be 16/(-28)*((-33)/(-22))/(-3). Let 2/7 + 1/7*m - 1/7*m**3 - p*m**2 = 0. Calculate m.
-2, -1, 1
Factor 1434*s**3 - s**4 - 2 + 8*s + 2 - 2*s**2 - 1439*s**3.
-s*(s - 1)*(s + 2)*(s + 4)
Let i be (19*9/(-3))/(1 + 0). Let k = 172/3 + i. Factor 1/3*b**5 - 2/3*b**2 + 1/3 - 2/3*b**3 + 1/3*b + k*b**4.
(b - 1)**2*(b + 1)**3/3
Suppose -309 + 315 = 3*d. Let l be (-425)/(-153) + d*(-1)/(-9). Solve -9/7*j**2 + 3/7*j**4 + 3/7*j + 6/7 - 3/7*j**l = 0 for j.
-1, 1, 2
Let i(k) = -k**2 + 7*k - 1. Let j be i(4). Suppose -3*y + 1 = -j. What is t in -t**y - 5*t**2 + 2*t - 2*t**3 + 6*t**3 + 0*t**2 = 0?
0, 1, 2
Let y(h) = -11*h**5 + 44*h**4 - 89*h**3 + 64*h**2 - 16*h - 8. Let s(q) = q**5 + q + 2. Let u(b) = 12*s(b) + 3*y(b). What is c in u(c) = 0?
0, 2/7, 1, 2, 3
Factor 1/2*j**5 + 0 + 0*j**2 + 0*j - 9/2*j**3 - 4*j**4.
j**3*(j - 9)*(j + 1)/2
Let r(q) = -3*q - 5. Let v be r(-5). Suppose -v*z = -6*z - 16. Factor 0*p - 4*p**2 + z*p + 0*p + p**3.
p*(p - 2)**2
Factor -1/4*d**3 + 0 - 2*d + 3/2*d**2.
-d*(d - 4)*(d - 2)/4
Factor 1/2*v**2 - 71/2*v + 35.
(v - 70)*(v - 1)/2
Let k(m) = -m**3 + 9*m**2 + 10*m + 6. Let x(d) = 2*d**3 - 17*d**2 - 21*d - 13. Let w(p) = -11*k(p) - 6*x(p). Find f such that w(f) = 0.
-2, -1, 6
Suppose 16*l - x = 19*l - 11, 5*l = 2*x + 22. Let z(r) be the second derivative of -4*r**2 + 0 + 4/3*r**3 + 3*r - 1/6*r**l. Factor z(k).
-2*(k - 2)**2
Let i(p) be the first derivative of 17/18*p**3 + 2/3*p + 5/3*p**2 + 6 + 1/6*p**4. Factor i(k).
(k + 2)**2*(4*k + 1)/6
Let y = 604 + -601. Determine q so that -12/13*q**y + 2/13*q**2 + 10/13*q**4 + 0*q + 0 + 24/13*q**5 = 0.
-1, 0, 1/4, 1/3
Let f be ((-82)/(-10) + -5)*((-54)/(-12) - 4). Solve 6/5*p**2 - 8/5*p - f + 4/5*p**3 - 2/5*p**4 = 0 for p.
-1, 2
Let u(m) be the first derivative of -m**3/30 - 7*m**2/10 - 49*m/10 - 32. Determine o, given that u(o) = 0.
-7
Let y(b) be the first derivative of b**5/20 + 7*b**4/16 - b**3/12 - 7*b**2/8 - 266. Factor y(z).
z*(z - 1)*(z + 1)*(z + 7)/4
Let y(s) be the third derivative of 0 + 4*s**2 - 1/105*s**7 + 0*s**3 + 0*s + 3/32*s**4 + 1/1344*s**8 - 1/10*s**5 + 11/240*s**6. Find i, given that y(i) = 0.
0, 1, 3
Let u = 14 + -12. Let q(r) = 3*r + 3. Let f be q(u). Factor f*j**3 - 6*j**2 + j + 0*j**4 + 0*j - 4*j**4 + 0*j**4.
-j*(j - 1)**2*(4*j - 1)
Let j(m) be the first derivative of -3 + 48*m**2 + 8*m + 169/3*m**6 + 226/3*m**3 - 217/2*m**4 - 234/5*m**5. Find h such that j(h) = 0.
-1, -2/13, 1
Let g(y) = 5*y**3 + 22*y**2 - 67*y. Let c(l) = 10*l**3 + 45*l**2 - 135*l. Let h(a) = 3*c(a) - 5*g(a). Factor h(u).
5*u*(u - 2)*(u + 7)
Let p(n) be the first derivative of -n**6/2 - 24*n**5/5 - 27*n**4/2 - 16*n**3 - 15*n**2/2 + 372. What is w in p(w) = 0?
-5, -1, 0
Let a(i) be the second derivative of i**7/21 + 8*i**6/15 + 12*i**5/5 + 17*i**4/3 + 23*i**3/3 + 6*i**2 + 2*i + 89. Suppose a(t) = 0. What is t?
-3, -2, -1
Suppose 0 = -181*p + 177*p. Let f(w) be the first derivative of -6/5*w**5 - 3/4*w**4 + p*w**3 - 1 + 0*w + 0*w**2 - 1/2*w**6. Factor f(v).
-3*v**3*(v + 1)**2
Determine l, given that -238 + 25*l**3 + 5*l**4 + 70*l + 148 + 5*l**2 - 175*l = 0.
-3, -1, 2
Let a(r) be the second derivative of -5*r**7/42 - 13*r**6/30 + 3*r**5/10 + 30*r. Solve a(y) = 0.
-3, 0, 2/5
Factor 2/7*t**2 + 68/7*t + 578/7.
2*(t + 17)**2/7
Let r = 2281/4 + -38753/68. Suppose 0*j + 2/17*j**4 + r*j**3 + 0 + 4/17*j**2 = 0. What is j?
-2, -1, 0
Let v(t) be the first derivative of -t**6/360 + t**5/45 - 5*t**4/72 + t**3/9 + 5*t**2 + 6. Let y(f) be the second derivative of v(f). Factor y(s).
-(s - 2)*(s - 1)**2/3
Let s(o) be the second derivative of o + 1/3*o**3 + 7/12*o**4 + 0 + 3/20*o**5 - 7/30*o**6 + 0*o**2 - 5/42*o**7. Find z, given that s(z) = 0.
-1, -2/5, 0, 1
Let d(y) = -y**2 - 3*y + 6. Let n be 18/(-6)*(-2 + 3). Let j be d(n). Find l, given that -2*l**2 + 2/9*l**3 + j*l - 6 = 0.
3
Suppose -3*z = -0 - 3. Let r(l) = 2*l**3 + 2*l**2 - 1. Let u be r(z). Factor j**u - 3 - j + 2 - 16*j**2 + 17*j**2.
(j - 1)*(j + 1)**2
Let a(d) be the second derivative of d**5/20 - 25*d**4/108 - 43*d**3/9 - 28*d**2/9 - 340*d. Suppose a(x) = 0. Calculate x.
-4, -2/9, 7
Let z(u) = 3*u + 1. Let d be z(1). Let 20*b - 11*b + d + 10*b**2 - 8*b - 15*b = 0. Calculate b.
2/5, 1
Let b(g) = 2*g**3 + 2*g**2 - 4*g - 6. Let d(x) = -6*x**2 - 5*x**3 - 2*x + 14*x - 4*x**2 + 19 + 5*x**2. Let i(s) = -7