Let n(h) = h**3 - 2*h**2 + h. Let o be n(0). Let g be (-5)/28 - (-3)/7. Let g*a**2 + o*a - 1/4 = 0. What is a?
-1, 1
Let h(n) be the third derivative of -n**6/200 + 2*n**5/25 - 3*n**4/10 + 5*n**2 + 3. Factor h(q).
-3*q*(q - 6)*(q - 2)/5
Let d be 4165/140 - 30 - (-13)/4. Suppose -6/7*z**2 + 3/7*z**d + 3/7*z + 0 = 0. Calculate z.
0, 1
Let p(r) be the third derivative of 0*r - 2/5*r**3 + 0 - 23*r**2 - 1/100*r**5 - 1/10*r**4. Find o, given that p(o) = 0.
-2
Let l be 2*(0 + (-5)/(-2)). Let u = 74 + -69. Find z such that -z**l - 2*z**4 - z**4 + 3*z**2 - 3*z**u + 3*z**3 + z**5 = 0.
-1, 0, 1
Let v = -137 - -421/3. Determine n, given that 2/3*n**4 + 8/3*n - 16/3 - v*n**3 + 4*n**2 = 0.
-1, 2
Let u(o) be the second derivative of o**9/3780 - o**8/560 + o**7/630 + o**6/60 - o**5/15 - o**4 + 14*o. Let i(v) be the third derivative of u(v). Factor i(l).
4*(l - 2)*(l - 1)**2*(l + 1)
Suppose 0 = -3*t - 3*i, -2 = -3*t - 2*i - 4. Let v(b) = -2*b**3 + 5. Let r(w) = w**3 - w - 1. Let d(n) = t*v(n) - 6*r(n). Suppose d(f) = 0. Calculate f.
-2, 1
Let c = -125/7 - -2431/133. Factor -10/19*u - 2/19*u**3 - c*u**2 - 4/19.
-2*(u + 1)**2*(u + 2)/19
Let o(b) be the first derivative of -9/4*b**4 + 1/2*b**6 - 4*b**3 + 0*b - 27 + 6*b**2 + 6/5*b**5. Factor o(v).
3*v*(v - 1)**2*(v + 2)**2
Suppose -20 = -5*s + 5. Let -10*f**4 + 0*f**2 + 5*f**3 - s*f + 5*f**4 + 5*f**2 = 0. What is f?
-1, 0, 1
Let s = -1/17354 + 104131/121478. Let 3/7*l**5 + 9/7*l - 6/7*l**2 - 12/7*l**3 + 0*l**4 + s = 0. Calculate l.
-1, 1, 2
Let x(p) be the first derivative of p**5/20 - 3*p**4/4 + 9*p**3/2 - 3*p**2 + 14. Let b(u) be the second derivative of x(u). Factor b(n).
3*(n - 3)**2
Let j be (-14)/(-5) - ((-33)/15 - -3). Let i(u) be the second derivative of -8*u + 0 + 1/48*u**4 + 0*u**3 - 1/8*u**j. Factor i(x).
(x - 1)*(x + 1)/4
Factor 1888/5 + 7104*d**2 - 14176/5*d - 5960*d**3 + 50*d**4.
2*(d - 118)*(5*d - 2)**3/5
Let a be (-23)/92 - (-33)/4. Factor -2*d + 4*d - 2*d**3 + 3*d**2 - 3*d**2 + a - 8*d**2.
-2*(d - 1)*(d + 1)*(d + 4)
Find w, given that -156/5 - 952/5*w**2 - 172/5*w**4 + 4/5*w**5 + 648/5*w**3 + 628/5*w = 0.
1, 39
Let w = 4895 - 9789/2. Factor -w*x**2 + 0 + 0*x - 1/4*x**3.
-x**2*(x + 2)/4
Let a(i) be the first derivative of 0*i**3 - 3/5*i**4 + 12 + 0*i**2 - 9/25*i**5 + 1/10*i**6 + 0*i. Factor a(z).
3*z**3*(z - 4)*(z + 1)/5
Suppose 0 = -3*s + 3*y + 24, s = -3*y + 2*y + 6. Suppose 9*j - s*j = 6. Factor 2*b**4 + 2*b**5 + b**j + 5*b**2 - 3*b**3 - 7*b**2.
2*b**2*(b - 1)*(b + 1)**2
Let a(d) = 6*d**5 - 21*d**3 + 6*d**2 + 18*d - 12. Let h(u) = -6*u**5 - u**4 + 21*u**3 - 5*u**2 - 17*u + 10. Let m(o) = 2*a(o) + 3*h(o). Solve m(x) = 0 for x.
-2, -1, 1/2, 1
Factor -8/9*q**2 - 1/9*q**3 - 5/9*q + 50/9.
-(q - 2)*(q + 5)**2/9
Factor 1/9*a**3 + 0 - 50/9*a**2 + 625/9*a.
a*(a - 25)**2/9
Let t(r) be the second derivative of r**8/4480 - r**6/40 + r**5/5 + 7*r**4/6 - 7*r. Let p(i) be the third derivative of t(i). Factor p(f).
3*(f - 2)**2*(f + 4)/2
Let m(h) be the second derivative of 2/3*h**3 + 0*h**5 + 0*h**2 - 20*h - 1/15*h**6 + 0 + 1/2*h**4. Suppose m(t) = 0. What is t?
-1, 0, 2
Let l(p) be the first derivative of -2*p**3/33 - 42*p**2/11 - 882*p/11 + 39. Determine s, given that l(s) = 0.
-21
Let z = 697/2217 + 14/739. Find d such that 1/2*d + z + 1/6*d**2 = 0.
-2, -1
Let l(j) be the second derivative of -1/30*j**5 + 4/9*j**3 + 0 + 1/9*j**4 - 8/3*j**2 - 19*j. Let l(f) = 0. Calculate f.
-2, 2
Let z(f) be the first derivative of 2*f**5/45 + f**4/18 - 10*f**3/27 + f**2/3 - 115. Factor z(n).
2*n*(n - 1)**2*(n + 3)/9
Suppose 3*n - 24 = -0*n + 3*r, -3*r - 9 = 0. Let b(g) be the second derivative of -1/8*g**4 + 3/40*g**n + 1/20*g**6 - 1/4*g**3 + 0*g**2 + 0 - 6*g. Factor b(u).
3*u*(u - 1)*(u + 1)**2/2
Let i(k) be the third derivative of -k**9/30240 + k**8/2016 - k**7/630 - 11*k**5/60 + 22*k**2. Let j(a) be the third derivative of i(a). Factor j(b).
-2*b*(b - 4)*(b - 1)
Find u such that 0 + 2/9*u**3 - 20/9*u**2 + 2/9*u**4 + 16/9*u = 0.
-4, 0, 1, 2
Suppose 0*h - 4*h = -2*x - 20, -x = -5*h + 22. Determine f so that 16*f + 40*f + 263 - 67 + h*f**2 = 0.
-7
Let n be (3/(-52))/(3/(-2)). Let g(q) be the third derivative of -3/13*q**3 + 0 - 1/390*q**5 - n*q**4 + 0*q - 3*q**2. Factor g(b).
-2*(b + 3)**2/13
Let i(n) be the second derivative of -n**5/160 - n**4/12 - 5*n**3/48 + 7*n**2/8 - 21*n. Suppose i(x) = 0. What is x?
-7, -2, 1
Suppose 0*d**2 - 4/3*d**3 - 14/9*d**4 + 0 + 0*d - 2/9*d**5 = 0. What is d?
-6, -1, 0
Suppose -u = -0*u + o + 5, -5 = -4*u + o. Let l(m) be the third derivative of 0*m**4 + 0*m + 1/660*m**6 - 1/165*m**5 + u + 11*m**2 + 0*m**3. Factor l(w).
2*w**2*(w - 2)/11
Let v(h) be the second derivative of -13*h**4/3 - 4*h**3/3 - 2*h - 33. Factor v(r).
-4*r*(13*r + 2)
Suppose 9*m - 3 = 42. Let z(l) be the second derivative of 3/4*l**4 - 3/2*l**3 + 3/2*l**2 - 3/20*l**m + 0 + 9*l. Let z(r) = 0. Calculate r.
1
Determine p so that 1 + 1/6*p**3 - 5/6*p - 1/3*p**2 = 0.
-2, 1, 3
Let z(x) be the third derivative of x**6/120 + x**5/20 - 7*x**3/6 + 23*x**2. Let i(r) be the first derivative of z(r). What is j in i(j) = 0?
-2, 0
Let l(q) be the second derivative of 5*q**4/6 - 155*q**3/12 + 105*q**2/4 + 425*q. Factor l(p).
5*(p - 7)*(4*p - 3)/2
Let r = 169 + -165. Suppose 0 = 2*m + 5*t - 4*t - 4, 4*m - t = -r. What is k in -3/2*k + m + 9/2*k**2 = 0?
0, 1/3
Let v(r) = r**4 - r**3 + r. Let s(m) = 5*m**5 - 20*m**3 + 5*m**2 + 15*m. Let i(q) = -s(q) + 5*v(q). Let i(p) = 0. Calculate p.
-1, 0, 1, 2
Let s(g) = 30*g**4 + 64*g**3 + 34*g**2 + 2*g - 2. Let k(z) = 2*z**5 - z**4 - 2*z**3 + z**2 - z + 1. Let y(h) = 2*k(h) + s(h). Suppose y(v) = 0. What is v?
-3, -1, 0
Let a be (-120)/56 - 3/(-1). Factor 4/7 + a*v - 4/7*v**2.
-2*(v - 2)*(2*v + 1)/7
Let f(v) = 3*v - 37. Let q be f(12). Let m(y) = -8*y**2 - 52*y - 144. Let x(l) = l**2 + l. Let w(r) = q*m(r) - 4*x(r). Determine p so that w(p) = 0.
-6
Let m = 936 - 931. Let i(j) be the third derivative of -1/12*j**4 + 1/120*j**6 + 0*j - 1/60*j**m - j**2 + 0*j**3 + 0. What is c in i(c) = 0?
-1, 0, 2
Factor 16/3*b + 40/9 + 2*b**2 + 2/9*b**3.
2*(b + 2)**2*(b + 5)/9
Suppose 5*v + 4*o + 12 = 0, -o = -4*v + 4*o + 15. Let m = 985/3 - 327. Factor -4/3*b**2 + v + m*b.
-4*b*(b - 1)/3
Let i(q) be the third derivative of -q**8/3024 + q**7/270 + q**6/90 - 7*q**5/135 - 4*q**4/27 + 11*q**2 - 22. What is a in i(a) = 0?
-2, -1, 0, 2, 8
Factor -45270 + 45270 + 20*g**3 - 5*g**4 - 5*g**2 - 30*g.
-5*g*(g - 3)*(g - 2)*(g + 1)
Let s(z) = -z + 14. Let f be s(10). Let r be f/(-8)*(-6)/1. Let -r - 11*o**3 - 45*o**2 - 20*o**3 - 2*o**3 + 48*o**4 + 24*o + 9*o**3 = 0. What is o?
-1, 1/4, 1
Let v be 4984/(-5340)*80/(-14). Factor 4/3*s**2 - v*s + 16/3.
4*(s - 2)**2/3
Suppose 5*u - 59 = -4*q - 11, -4*u - 4*q + 40 = 0. Let r = -6 + u. Suppose -3*n**2 + 0*n**r + n**4 + 2*n**4 = 0. Calculate n.
-1, 0, 1
Let j(b) be the second derivative of b**8/2240 - b**7/1120 + 47*b**3/6 + 22*b. Let m(n) be the second derivative of j(n). Find h, given that m(h) = 0.
0, 1
Let t(w) = w**2 - 8*w - 9. Let v be t(9). Suppose 4*m - 7 - 9 = v. Suppose -2*h**2 + 0*h**2 + 4*h**2 - 2*h**m = 0. Calculate h.
-1, 0, 1
Suppose -90 = -3*v - 3*v. Let z be ((-2)/v)/(17/(-51)). Factor 2/5 - 2/5*x**2 - z*x**3 + 2/5*x.
-2*(x - 1)*(x + 1)**2/5
Factor -1/2*b**2 + 13/2 + 6*b.
-(b - 13)*(b + 1)/2
Let h be -2*((-1)/(-4) - 39/12). Let b(c) be the second derivative of 0 + 1/12*c**4 + 0*c**2 + 1/6*c**3 - 1/20*c**5 + c - 1/30*c**h. Find k such that b(k) = 0.
-1, 0, 1
Let t(j) be the second derivative of -j**5/80 + j**4/12 + 11*j**3/24 + 3*j**2/4 - 50*j. Solve t(f) = 0.
-1, 6
Let j(l) be the second derivative of 3*l**5/50 - 26*l**4/5 + 149*l**3/5 - 294*l**2/5 + l + 171. Find s such that j(s) = 0.
1, 2, 49
Let -100*z**2 + 10*z**3 + 252*z - 192*z + 6*z**3 - z**3 = 0. What is z?
0, 2/3, 6
Let t be ((-352)/28 - -15) + 4. Factor 72/7*q**2 + 6/7 + t*q - 48/7*q**3.
-3*(q - 2)*(4*q + 1)**2/7
Let i(q) be the second derivative of -5*q**4/12 - 131*q**3/3 - 52*q**2 + 73*q. Factor i(d).
-(d + 52)*(5*d + 2)
Suppose -5*t - 2*c - 202 = 0, -3*c + 116 = -3*t + c. Let m be 10/55 + t/(-22). Let f + f**2 + f**4 + f - 3*f - m*f**4 + f**3 = 0. Calculate f.
-1, 0, 1
Let k(v) be the second derivative of -v**6/15 + 6*v**5/5 + 43*v**4/6 + 10*v**3 + 145*v. Factor k(w).
-2*w*(w - 15)*(w + 1)*(w + 2)
Suppose 