0 = 0.
0, 6
Let h = -41 + -10. Let f = h + 61. Let -5399 - 2*t**4 + 5399 + 0*t**2 + 12*t**3 - f*t**2 = 0. What is t?
0, 1, 5
Let m(p) be the second derivative of p**8/1512 - p**6/540 - 21*p**2 + 29*p - 1. Let f(n) be the first derivative of m(n). Factor f(h).
2*h**3*(h - 1)*(h + 1)/9
Let o(l) be the first derivative of 3/2*l**2 + 1 - l**3 - 3/4*l**4 + 3*l. Determine m, given that o(m) = 0.
-1, 1
Let h be 3/((-40)/(-16) + -2). Let q(y) = 4*y**2 - 25*y + 9. Let o be q(h). Suppose -9/7*v**4 + 36/7*v - 30/7*v**o + 12/7 - 9/7*v**2 = 0. What is v?
-2, -1/3, 1
Let r(o) be the second derivative of -o**5/270 + o**4/12 + 61*o**2 + 237*o. Let l(s) be the first derivative of r(s). Suppose l(f) = 0. Calculate f.
0, 9
Let n(j) be the first derivative of -j**6/6 + 33*j**5/5 - 147*j**4/4 + 199*j**3/3 - 42*j**2 + 2070. What is m in n(m) = 0?
0, 1, 3, 28
Let q(y) = y + 9. Let n be q(-6). Suppose -31*s - 85*s = -7*s - 545. Factor -3*m**4 + 0*m + 45/7*m**n + 3/7*m**s + 0 - 27/7*m**2.
3*m**2*(m - 3)**2*(m - 1)/7
Let h(n) = 20*n**4 - 92*n**3 + 1443*n**2 - 2537*n + 1217. Let t(z) = 7*z**4 - 30*z**3 + 481*z**2 - 846*z + 406. Let l(c) = 6*h(c) - 17*t(c). Factor l(w).
(w - 20)**2*(w - 1)**2
Let q(g) = -4*g**2 - 296*g + 4. Let i be q(-74). Let v(a) be the second derivative of 1/4*a**i - 16*a + 24*a**2 + 0 - 4*a**3. Factor v(z).
3*(z - 4)**2
Let p(k) be the second derivative of -k**7/70 + 3*k**6/25 + 12*k**5/25 - 547*k. Factor p(r).
-3*r**3*(r - 8)*(r + 2)/5
Factor s**3 + 364*s - 286*s**2 - 2610 - 17284 - 20434 + 20368*s.
(s - 142)**2*(s - 2)
Let t be (-36 - -6)/((-440)/704). Let y(l) be the first derivative of 0*l**2 + 0*l**3 + 3/5*l**4 + 12/25*l**5 + 1/10*l**6 + 0*l + t. Factor y(o).
3*o**3*(o + 2)**2/5
Let i = -447 - -46044/103. Let c = i + 85/618. Find k such that -c*k**2 + 0 - 1/3*k = 0.
-2, 0
Suppose -835 - 1005 = -728*f + 1122 - 778. Solve 5*y**4 - 5/4*y**5 + 0*y**f + 15/2 + 5/4*y - 25/2*y**2 = 0 for y.
-1, 1, 2, 3
Suppose 15*q - 16 = 7*q. Let r(n) = n**3 + n**2. Let o(f) = 41*f - 57*f + 14*f**3 - 9*f**2 - f**3. Let k(v) = q*o(v) - 6*r(v). Factor k(z).
4*z*(z - 2)*(5*z + 4)
Let y(d) be the third derivative of d**5/15 - 98*d**3/3 - 219*d**2. Factor y(j).
4*(j - 7)*(j + 7)
Let o(a) be the second derivative of -25*a**4 + 0 + 145*a + 0*a**3 + 3*a**5 + 0*a**2 - 1/10*a**6. Factor o(g).
-3*g**2*(g - 10)**2
Let q(u) be the third derivative of 0*u**3 - u - 1/2*u**5 - 1/48*u**6 + 65/48*u**4 + 34*u**2 + 0. Factor q(s).
-5*s*(s - 1)*(s + 13)/2
Let n(x) = 39*x**3 + 6*x**2 - 4. Let m(d) = -19*d**2 + 7*d**3 + 7 - 123*d**3 + 7 - 3. Let w(v) = 4*m(v) + 11*n(v). Factor w(j).
-5*j**2*(7*j + 2)
Determine a, given that -648 - 504*a**2 - 918*a - 16*a**4 - 2/3*a**5 - 132*a**3 = 0.
-12, -3
Let w = 533 + -531. Solve -75*x + 47*x - 4*x**3 + 0*x**3 - 20 - 15 - 37 + 40*x**w = 0 for x.
-1, 2, 9
Let q(y) be the second derivative of -y - 25/102*y**4 + 0*y**3 + 1/255*y**6 + 0*y**5 - 7 + 0*y**2. Suppose q(u) = 0. What is u?
-5, 0, 5
Let h(r) be the first derivative of r**3 + 2916*r**2 + 2834352*r + 35. Factor h(q).
3*(q + 972)**2
Let p(d) be the third derivative of -d**6/60 - 499*d**5/15 + 333*d**4/4 + 5983*d**2. Factor p(g).
-2*g*(g - 1)*(g + 999)
Let g(c) be the first derivative of 80 - 125/2*c**2 + 0*c - c**5 - 25*c**3 + 45/4*c**4. Find n such that g(n) = 0.
-1, 0, 5
Let y(f) be the second derivative of 1/90*f**6 + 0*f**2 + 49/12*f**4 + 0 - 343/18*f**3 + 105*f - 7/20*f**5. Let y(t) = 0. What is t?
0, 7
Let p(y) be the first derivative of y**5/150 + 17*y**4/60 + 27*y**2 + 55. Let w(i) be the second derivative of p(i). Find d, given that w(d) = 0.
-17, 0
Let t(v) be the first derivative of 2*v**3/15 - 142*v**2/5 + 112*v - 1117. Factor t(g).
2*(g - 140)*(g - 2)/5
Let h(q) = -121*q**2 + 2*q + 3. Let g(z) = 62*z**2 + z - 1. Let o(i) = -2*g(i) - h(i). Factor o(l).
-(l + 1)*(3*l + 1)
Let g(v) be the first derivative of 6 + 0*v + 1/3*v**3 + 0*v**2. Solve g(t) = 0 for t.
0
Let o = 254/1181 - -17956/15353. Suppose -6/13*h + o*h**3 - 8/13*h**4 + 20/13*h**2 + 0 = 0. What is h?
-1, 0, 1/4, 3
Let j(l) be the third derivative of 361*l**6/90 - 5738*l**5/45 - 607*l**4/18 - 32*l**3/9 + 479*l**2. Factor j(n).
4*(n - 16)*(19*n + 1)**2/3
Let m(k) = -7*k**3 + 68*k**2 + 67*k + 8. Let a(b) = -2*b**3 + 2. Let p(c) = -4*a(c) + m(c). Factor p(l).
l*(l + 1)*(l + 67)
Factor -8*u**4 + 529/6*u + 311/3*u**3 + 1/6*u**5 - 184*u**2 + 0.
u*(u - 23)**2*(u - 1)**2/6
Suppose 9*o - 11 = 7. Factor -2*f**5 + o*f**5 - 14*f**3 + f**5 - 5*f**4 + 13*f**3 + 5*f**2.
f**2*(f - 5)*(f - 1)*(f + 1)
Let u be ((-265716)/112)/(-11) + 1/(-4). Let b = -215 + u. Factor 6/7 - b*z - 3/7*z**2.
-3*(z - 1)*(z + 2)/7
Let g be 1/33 - (-2077)/10230. Let f(r) be the second derivative of 9*r - 5/6*r**3 - 3/4*r**4 + r**2 + 1/4*r**5 + 0 + g*r**6. Determine z, given that f(z) = 0.
-1, 2/7, 1
Let b(m) be the second derivative of m**5/10 + 5*m**4/6 + 4*m**3/3 + 171*m + 1. Factor b(n).
2*n*(n + 1)*(n + 4)
Let h(u) be the second derivative of -u**6/50 + 9*u**5/25 - 7*u**4/4 + 12*u**3/5 - 2276*u. Factor h(d).
-3*d*(d - 8)*(d - 3)*(d - 1)/5
Let g = -7693 + 184633/24. Let v(s) be the third derivative of 10*s**2 - 1/4*s**5 + 0*s**3 + 5/6*s**4 + 0 + 0*s - g*s**6. Factor v(u).
-5*u*(u - 1)*(u + 4)
Solve -9/5*y**3 - 3/5*y**4 + 0 - 84/5*y + 72/5*y**2 = 0 for y.
-7, 0, 2
Suppose -4/5*w**5 + 52/5*w**4 + 368/5*w**2 - 224/5*w + 0 - 216/5*w**3 = 0. What is w?
0, 2, 7
Suppose 42 = -4*j + j. Let w be j/(-21)*(-6)/(-4) + 11. Suppose 10*r**2 + 8 - 6*r - 5*r**2 - 7*r**2 + w = 0. Calculate r.
-5, 2
Let w**3 - 60*w + 2*w**2 - 17*w**2 - 35*w**2 + 43*w**2 = 0. Calculate w.
-5, 0, 12
Let m(l) be the third derivative of l**6/180 + 331*l**5/30 + 20584*l**4/3 + 246016*l**3/9 + 1380*l**2. Suppose m(d) = 0. Calculate d.
-496, -1
Suppose 12*h - 4 = 11*h. Factor -759*o**2 - 162*o - 518*o**3 - 139*o**4 - 35*o**h + 4 + 249*o**2.
-2*(o + 1)**3*(87*o - 2)
Let p = -2101 - -2104. Suppose p*o - 4 = -4*a, -3*o - 77*a + 78*a = 1. Factor 8/5*d + 1/5*d**4 + o + 6/5*d**3 + 12/5*d**2.
d*(d + 2)**3/5
Suppose -61/3*q**2 + 20/3 + 5/3*q**4 - 8*q - 4*q**3 = 0. Calculate q.
-2, -1, 2/5, 5
Let l be (-12)/(-21) + ((-128)/(-448))/(11 + -1). Factor 0 - 51/5*g**3 - 111/5*g**2 - 57/5*g + l*g**4.
3*g*(g - 19)*(g + 1)**2/5
Suppose 205*o + 129*o + 256*o = -89*o. Factor -6*k**4 + 39/2*k**3 + 0*k + 1/2*k**5 - 14*k**2 + o.
k**2*(k - 7)*(k - 4)*(k - 1)/2
Let j(d) be the second derivative of d**7/28 + 7*d**6/20 + 27*d**5/40 - 7*d**4/8 - 5*d**3/2 - 467*d - 4. Solve j(z) = 0 for z.
-5, -2, -1, 0, 1
Let a(c) be the second derivative of -c**5/5 + c**4/3 + 4*c**3 - 982*c. Suppose a(g) = 0. Calculate g.
-2, 0, 3
Let s(b) be the first derivative of 7*b**3 + 13299*b**2/2 + 3798*b + 633. Factor s(l).
3*(l + 633)*(7*l + 2)
Let l be (6 - 200/32) + (-2)/(-8). Suppose 0 = 2*f + 4*p - 20, -5*p = 5*f - l*p - 50. Solve 0*w**4 + f*w**3 + 6*w**3 + 5*w**3 + 3*w**4 = 0 for w.
-7, 0
Let h(t) be the third derivative of t**5/140 - 141*t**4/14 + 39762*t**3/7 + 1503*t**2. Factor h(r).
3*(r - 282)**2/7
Let n be (-2)/8 - ((-69645)/(-6300) - 20). Let u = n + -124/15. Factor 15/7*p + 6 - u*p**2.
-3*(p - 7)*(p + 2)/7
Find q such that 78 - 11 + 141 + 80 - 281498*q**2 + 41*q + 281499*q**2 = 0.
-32, -9
Let t = 361590 + -361587. Factor 32*z + 6*z**2 + 1/3*z**t + 128/3.
(z + 2)*(z + 8)**2/3
Let h(z) be the third derivative of -5*z**2 + 1 + 0*z + 15552/17*z**3 - 1/1785*z**7 + 3564/17*z**4 - 126/17*z**5 + 107/1020*z**6. Factor h(a).
-2*(a - 36)**3*(a + 1)/17
Let b(k) = k**3 - 9*k**2 + 4*k - 22. Let n be b(9). Let o be -12*((-42)/(-36) - 9/6). Factor -12*i + o*i**2 - n*i + 14*i - 16.
4*(i - 4)*(i + 1)
Let l(g) be the third derivative of g**7/70 + 43*g**6/24 - 81*g**5/5 + 101*g**4/2 - 152*g**3/3 + 3617*g**2. Let l(t) = 0. What is t?
-76, 1/3, 2
Factor -201*g**2 + 83*g - 480 + 199*g**2 - 19*g.
-2*(g - 20)*(g - 12)
Let h(m) be the first derivative of 15/4*m**4 + 3/5*m**5 + 80 - 18*m - 15/2*m**2 + 5*m**3. Solve h(s) = 0.
-3, -2, -1, 1
Let s be -54*(-23 - (-17476)/765). Factor 33/5*i + s*i**2 + 6/5.
3*(2*i + 1)*(7*i + 2)/5
Let b(h) = -4*h + 150. Let m be b(37). Factor -21*r**3 + m*r**2 + 17*r**4 + 19*r**4 - 124*r**5 + 107*r**5.
-r**2*(r - 1)**2*(17*r - 2)
Let k(v) be the second derivative of -v**7/189 - v**6/135 + v**5/18 - v**4/18 + 1533*v. Suppose k(f) = 0. Calcul