35 + 13*p**6/420 + p**5/15 + 252*p**2. What is w in x(w) = 0?
-1, 0, 14
Let a(b) be the second derivative of 0 + 5/6*b**3 + 0*b**2 + 20*b + 1/3*b**4 + 1/15*b**6 + 13/30*b**5. Let x(m) be the second derivative of a(m). Factor x(y).
4*(y + 2)*(6*y + 1)
Determine k, given that -150/13*k + 2/13*k**4 - 2*k**3 + 0 + 110/13*k**2 = 0.
0, 3, 5
Let t = 1216 + -17023/14. Let h(b) be the second derivative of 1/70*b**6 + 3/140*b**5 + 0*b**2 + 0*b**3 + 8*b + 0 - t*b**4. Suppose h(r) = 0. What is r?
-2, 0, 1
Let o(l) be the second derivative of 4*l**2 + 0 - 5/6*l**4 - 1/3*l**3 + 130*l. Factor o(q).
-2*(q + 1)*(5*q - 4)
Let d = 1717/2 + -36053/42. Determine q so that -8/21 + 16/21*q - 10/21*q**2 + d*q**3 = 0.
1, 2
Let -39/7*f**3 + 12/7*f**4 + 3/7*f**5 + 0 - 12/7*f**2 + 36/7*f = 0. What is f?
-6, -1, 0, 1, 2
Let j(m) = -20*m**4 + 12*m**3 + 24*m**2 + 8*m - 24. Let n(i) = i**4 + i**3 + 3*i**2 + 3*i + 1. Let x(a) = -j(a) - 24*n(a). Let x(z) = 0. What is z?
-5, -2, 0
Let f = 9768 + -9763. Let t(p) be the second derivative of -3/160*p**f + 1/16*p**4 + 3*p - 3/8*p**2 + 1/16*p**3 + 0. Factor t(m).
-3*(m - 2)*(m - 1)*(m + 1)/8
Let c be (-5)/2*(59829/925 - 65). Find m such that c - 9/5*m**4 - 5*m**3 + 16/5*m + 9/5*m**5 + m**2 = 0.
-1, -2/3, -1/3, 1, 2
Let 222*y**2 + 0 + 0*y - 1/2*y**3 = 0. Calculate y.
0, 444
Let m = -313655 + 313655. Let -2/3*v**2 + m - 2*v = 0. Calculate v.
-3, 0
Let l(d) = 4*d**2 - 2970*d + 2969. Let b be l(1). Factor -238*t - 6/7*t**b - 578/7 + 202/7*t**2.
-2*(t - 17)**2*(3*t + 1)/7
Let m(g) be the first derivative of 2*g**3/15 - 3806*g**2/5 + 7242818*g/5 - 6799. Factor m(l).
2*(l - 1903)**2/5
Suppose 0 = -2*k + 3*x - 9, 74*x - 6 = 3*k + 72*x. Let c(q) be the third derivative of -10*q**2 + k + 0*q - 5/36*q**4 + 1/180*q**5 - 11/18*q**3. Factor c(a).
(a - 11)*(a + 1)/3
Solve 4/3*k - 5/3*k**2 + 20/3 - 1/3*k**3 = 0.
-5, -2, 2
Let r(q) be the first derivative of q**6/180 + q**5/15 - q**4 + 32*q**3/3 - 2*q - 22. Let y(z) be the third derivative of r(z). Factor y(m).
2*(m - 2)*(m + 6)
Let v(y) = 3*y**3 - 32*y**2 + 29*y. Let q(g) = 0*g**3 - 230*g - 16*g**2 + g**3 + 245*g. Let c(s) = 7*q(s) - 3*v(s). What is i in c(i) = 0?
-9, 0, 1
Suppose -14*y = -35*y + 210. Let b be 74/510*y - 8/6. Determine q, given that 18/17 + 12/17*q + b*q**2 = 0.
-3
Let q(o) = 39*o - 154. Let t be q(4). Suppose 5 - 6*c**t - 1894*c**3 + 6*c + 6*c + 1895*c**3 - 13 = 0. What is c?
2
Factor -87/4*l**2 - 23/2 - 113/4*l - 19/4*l**3 + 1/4*l**4.
(l - 23)*(l + 1)**2*(l + 2)/4
Let b = 919 - 929. Let y(i) = -30*i - 297. Let t be y(b). Suppose -6/11*x + 8/11*x**t - 4/11 + 0*x**4 - 2/11*x**5 + 4/11*x**2 = 0. Calculate x.
-1, 1, 2
Let g(a) be the first derivative of -16/3*a**3 + 5/72*a**6 + 0*a + 0*a**2 - 7 - 5/3*a**4 + 3/4*a**5. Let y(b) be the third derivative of g(b). Factor y(r).
5*(r + 4)*(5*r - 2)
Suppose -1764*d - 209*d**2 - 5*d**4 + 48*d**2 + 724*d - 227*d**2 + 3*d**4 + 62*d**3 = 0. What is d?
-2, 0, 13, 20
Let w(f) be the second derivative of 0*f**2 - f - 1/5*f**5 + 2*f**4 - 2 - 6*f**3. Suppose w(n) = 0. What is n?
0, 3
Let m = -3/689 + 11039/3445. Let k = -553/5 - -111. Factor -2/5*j**2 + 24/5 + k*j**3 - m*j.
2*(j - 2)**2*(j + 3)/5
Let t be 5592/20 + 15/(-25). Factor -10*j + 2*j**3 + t - 135 - 136 + 4*j**2 - 4*j.
2*(j - 1)**2*(j + 4)
Solve 4/3*z**2 + 338688 - 1344*z = 0 for z.
504
Suppose 140*r = 122*r. Let p(d) be the first derivative of -2/9*d**2 + r*d - 10 - 4/27*d**3. Solve p(t) = 0 for t.
-1, 0
Suppose 2*n + 62 = 5*v, -2*n + 0*n - 38 = -3*v. Let p be (5 + -5)*3/v. Factor -1 - 35*z**2 + 5*z**3 + 2*z**4 + 38*z**2 + p + 0 - z.
(z + 1)**3*(2*z - 1)
Suppose 0 = 184*h - 189*h. Suppose h*w + 21 = w. Suppose -w*f - 6 + 13*f - 3*f**2 - f = 0. What is f?
-2, -1
Let d = -1032 + 932. Let c be (d/154)/(((-240)/(-105))/(-16)). Factor c - 8/11*r**3 - 180/11*r - 78/11*r**2.
-2*(r + 5)**2*(4*r - 1)/11
Let d(k) = -k**2 + 3*k + 6. Let h = -82 + 86. Let v be d(h). Factor 5*f**v - f**2 - 2*f**2 + 4*f.
2*f*(f + 2)
Let x(h) be the first derivative of h**3/3 + 3*h**2/2 + 3*h - 29. Let r be x(-3). Factor 9/5*n - 3/5 + 3/5*n**r - 9/5*n**2.
3*(n - 1)**3/5
Determine v so that 415*v**3 - 5*v**5 + 888419*v**2 - 887194*v**2 - 7*v**4 + 2*v**4 + 400 + 1210*v = 0.
-8, -1, 10
Let x(j) be the first derivative of 0*j**2 + 2/11*j - 2/33*j**3 - 104. Suppose x(n) = 0. What is n?
-1, 1
Let x(d) = d**3 - 46*d**2 - 69*d + 6. Let v(h) = h**3 - 34*h**2 - 68*h + 9. Let c(q) = 2*v(q) - 3*x(q). Let c(b) = 0. What is b?
-1, 0, 71
Let f(v) be the third derivative of 1/150*v**5 + 0*v - 217*v**2 + 0 + 361/15*v**3 - 19/30*v**4. Determine i so that f(i) = 0.
19
Solve 19/3*d**2 + 35 + 1/6*d**3 + 247/6*d = 0 for d.
-30, -7, -1
Suppose 4*a - 9*d + 10*d = 783, 0 = -3*a + 3*d + 591. Factor -43*v**2 + a*v - 186*v - 32*v**2.
-5*v*(15*v - 2)
Factor 726*n**4 + 26*n - 40*n**3 + 20*n**3 + 4*n - 731*n**4 - 720 + 179*n**2 - 4*n**2.
-5*(n - 3)**2*(n + 2)*(n + 8)
Solve 20*i - 3*i**3 + 6*i**3 + 56*i - 30*i**2 - i**4 - 2*i**3 - 56 + 2*i**4 = 0 for i.
-7, 2
Let k = -3/92752946 - 1030531603359/98132616868. Let f = -3/2116 - k. Factor 3/4*c**5 + 3/2 + 9/2*c**4 + 27/4*c + 12*c**2 + f*c**3.
3*(c + 1)**4*(c + 2)/4
Find q, given that 253/2*q**2 + 5/2*q**4 + 61*q**3 - 66 - 124*q = 0.
-22, -3, -2/5, 1
Suppose u - 3*u + 155 = -5*y + 42, -5*y - 65 = 0. Suppose 7*k + u*k**2 - 7*k**3 - 49/2 + 1/2*k**4 = 0. What is k?
-1, 1, 7
Suppose 6*i + 105/2*i**2 + 0 = 0. Calculate i.
-4/35, 0
Let x(q) be the second derivative of 0 + 0*q**2 + 55*q + 1/30*q**6 - 4*q**3 - 11/6*q**4 + 3/20*q**5. Factor x(w).
w*(w - 4)*(w + 1)*(w + 6)
Let w(z) be the second derivative of -z**4/3 + 8368*z**3/3 - 8752928*z**2 + 35*z - 7. Factor w(u).
-4*(u - 2092)**2
Find l such that -8/9*l**3 + 44/9*l + 14/9*l**2 - 16/3 - 2/9*l**4 = 0.
-4, -3, 1, 2
Let c(h) be the third derivative of h**5/210 + 1261*h**4/42 - h**2 - 10*h + 25. Factor c(v).
2*v*(v + 2522)/7
Let w(a) = 36*a + 2522. Let d be w(-70). Let i(j) be the first derivative of -3/8*j**d - 1/24*j**3 + 13 - 9/8*j. Factor i(y).
-(y + 3)**2/8
Let p be 335/(-65) - (6/39)/(-1). Let v be (5/(p/(-2)) + -4)*-1. What is n in -7*n - 23*n - 3*n**3 - 12 + 6*n - 15*n**v = 0?
-2, -1
Let m(c) be the third derivative of -c**6/80 + 19*c**5/20 + 39*c**4/16 + 17*c**2 + 4*c + 8. Suppose m(v) = 0. Calculate v.
-1, 0, 39
Find b such that 35/2*b**2 - 12275/2*b - 1755 = 0.
-2/7, 351
Let z be 165/(-11)*2/15*-3. Let y(f) be the second derivative of 0*f**2 + 0 + 19*f - 5/6*f**z + 5/3*f**3 + 5/42*f**7 - 35/12*f**4 + 9/4*f**5. Factor y(b).
5*b*(b - 2)*(b - 1)**3
Let p(c) be the first derivative of c**2/2 + 14*c + 7. Let l be p(-14). Factor l*u**2 + 0*u**2 - u**2 - 2*u.
-u*(u + 2)
Let k be -3 + -3 + 1/(4/508). Let u = 125 - k. Find l such that 22*l**3 + 3*l**u + 2*l**2 - 12*l**3 - 8*l**2 - 13*l**3 = 0.
-1, 0, 2
Let c = -276688 + 276690. Factor 2/3*r**c - 22/3*r + 56/3.
2*(r - 7)*(r - 4)/3
Let r(u) be the second derivative of -u**4/12 + 42*u**3 - 7938*u**2 - u + 31. Solve r(t) = 0.
126
Let u(i) = -22132*i - 110658. Let j be u(-5). Let 1/6*f**j - 3*f + 27/2 = 0. Calculate f.
9
Suppose 148 = 624*o - 580*o + 16. Let i(f) be the first derivative of -4/5*f**5 + 3*f**4 + 8*f - 6*f**2 - 4/3*f**o + 8. Factor i(u).
-4*(u - 2)*(u - 1)**2*(u + 1)
Let c(m) = m**4 + m**2 - m - 1. Let k(j) = 8*j**4 - 5*j**3 - 12*j**2 + 7*j + 2. Let y = -390 - -388. Let n(l) = y*c(l) - k(l). Find d, given that n(d) = 0.
-1, 0, 1/2, 1
Let t(y) be the first derivative of -y**5/10 + 11*y**4/4 - 23*y**3/2 - 143*y**2 - 338*y + 3316. Suppose t(s) = 0. Calculate s.
-2, 13
Let j(l) = -l**3 + 8*l**2 - 3*l - 66. Let s(f) = 4*f**3 - 24*f**2 - 4*f + 200. Let h(d) = 8*j(d) + 3*s(d). Factor h(w).
4*(w - 3)*(w - 2)*(w + 3)
Let t = -63 - -72. Suppose -239 + 185 = -t*j. Factor 3/4*s**4 - j*s**3 + 27/4 - 18*s + 33/2*s**2.
3*(s - 3)**2*(s - 1)**2/4
Let z(c) be the third derivative of c**7/42 - 13*c**6/24 + 5*c**5/6 + 5*c**4 + 2*c**2 + 31*c. Factor z(y).
5*y*(y - 12)*(y - 2)*(y + 1)
Suppose -m - 2*b + 5 = 3, -5*m + 10 = -3*b. Suppose -17*c + 15*c - 2 = 2*o, 3*c - 2*o = 17. Find h, given that m*h - 7*h + 5*h**c - 5*h**2 + 2*h - 7*h = 0.
-1, 0, 2
Suppose -2*o = m, 5*o - 21*m = -17*m. Factor 5/6*u**3 - 3/2*u + o - 1/2*u**2 - 1/6*u**4.
-u*(u - 3)**2*(u + 1)/6
Suppose 0 = 4*d + 4*q + 56, 4*q - 34 = 3*d + 3*q. Let i be ((-1)/(