0. Calculate r.
1
Let a(t) be the second derivative of -t**6/45 - t**5/30 + 13*t**4/18 + 25*t**3/9 + 4*t**2 + 19*t. Suppose a(w) = 0. What is w?
-3, -1, 4
Let s(a) = a**3 - 2*a**2 - 3*a. Let i be s(3). Suppose t - 4*t = i. Find l such that 8*l - 9*l**2 + 3*l**3 - l + t*l - l = 0.
0, 1, 2
Let p(a) be the first derivative of -1/24*a**3 - 49/8*a + 7/8*a**2 + 23. Determine u, given that p(u) = 0.
7
Suppose 0 = -144*k + 79*k + 195. Let a(j) be the first derivative of -j**4 + 8/9*j**k - 1/3*j**2 + 0*j + 8/15*j**5 - 1/9*j**6 + 1. Factor a(v).
-2*v*(v - 1)**4/3
Let p = -149 - -1343/9. Let d(m) = m**2 + 2*m. Let f be d(-3). Let 4/9*n**2 + 2/9*n**f + p*n + 0 = 0. What is n?
-1, 0
Let k(m) be the second derivative of m**6/120 + m**5/16 + m**4/8 - m - 15. Solve k(n) = 0.
-3, -2, 0
Let f = -2803 + 70089/25. Factor 6/25*x**4 + 2/5*x**2 - 2/25*x - f*x**3 + 0.
2*x*(x - 1)**2*(3*x - 1)/25
Let o = -30 + 41. Suppose -15 = -2*n - o. Solve 1/3*v**n - 2/3*v + 0 = 0.
0, 2
Let l(d) be the third derivative of -d**5/60 - 13*d**4/24 + 8*d**2. Let j be l(-13). Factor 3/2*t**2 + 9/2*t**3 + j - 3*t.
3*t*(t + 1)*(3*t - 2)/2
Factor -117*w**2 + 5 - 1187*w**3 - 30*w - 38*w**2 + 1367*w**3.
5*(w - 1)*(4*w + 1)*(9*w - 1)
Let p(h) be the second derivative of -h**5 - 218*h**4/3 - 4664*h**3/3 + 1936*h**2 - 2*h + 178. Suppose p(o) = 0. Calculate o.
-22, 2/5
Let s(k) be the first derivative of -k**5/240 - k**4/12 - 2*k**3/3 + 8*k**2 + 43. Let g(l) be the second derivative of s(l). Solve g(o) = 0.
-4
Let k(f) be the second derivative of -f**5/30 + 38*f**4/3 - 1444*f**3 + 13*f - 6. Factor k(c).
-2*c*(c - 114)**2/3
Factor -2/5*m**5 + 0*m**2 + 0*m**4 + 2/5*m**3 + 0*m + 0.
-2*m**3*(m - 1)*(m + 1)/5
Let s(j) = 2*j**3 - 3*j**2 + j + 1. Let r(t) = 16*t**3 - 11*t**2 - 59*t + 61. Let v(p) = 2*r(p) - 14*s(p). Factor v(c).
4*(c - 3)*(c - 1)*(c + 9)
Let t = 123 - 123. Let s(j) be the third derivative of t + 0*j + j**2 - 1/140*j**5 - 1/56*j**4 + 0*j**3. Let s(x) = 0. What is x?
-1, 0
Suppose -12537*v + 12549*v - 36 = 0. Suppose -2/5*k + 0 - 1/5*k**4 - k**2 - 4/5*k**v = 0. What is k?
-2, -1, 0
Let p(c) be the second derivative of 7*c**5/40 + 23*c**4/24 + 5*c**3/3 + c**2 + 5*c + 2. Find f, given that p(f) = 0.
-2, -1, -2/7
Let w(p) be the second derivative of p**5/60 + p**4/4 + 7*p**3/9 - 22*p - 1. Determine x, given that w(x) = 0.
-7, -2, 0
Suppose 0 = 27*l - 22*l - 35. Let n = 7 - 1. Factor 0*w**3 + w**2 + w**3 + n*w**3 - 4*w**2 + 5*w**4 - 2 - l*w.
(w - 1)*(w + 1)**2*(5*w + 2)
Let w(a) = -141*a**3 + 3015*a**2 - 11232*a - 5019. Let u(n) = -11*n**3 + 232*n**2 - 864*n - 386. Let f(t) = -27*u(t) + 2*w(t). Factor f(m).
3*(m - 8)**2*(5*m + 2)
Let j = -12997 + 12999. Factor 1/6*v - 2/3*v**5 - 3/2*v**3 - 11/6*v**4 - 1/6*v**j + 0.
-v*(v + 1)**3*(4*v - 1)/6
Factor -3456*n**2 + 3 - 3 + 688*n + 26299*n**3 - 21919*n**3 - 100*n**4.
-4*n*(n - 43)*(5*n - 2)**2
Let k(o) be the third derivative of o**8/336 - o**6/30 + 108*o**2. Find l, given that k(l) = 0.
-2, 0, 2
Let j be (-22)/(-176) + 2*1/16. Let u be 0 + 4 + (-3 - -2). Let 1/4*g**2 + j*g**u + 0*g + 0 = 0. What is g?
-1, 0
Let r be -4 + 130/(-45) - -8. Let x(y) be the first derivative of 1 - 4/3*y - r*y**3 - 7/3*y**2. Find l, given that x(l) = 0.
-1, -2/5
Let d(w) = -w**3 - 4*w**2 - 3*w - 9. Let l be d(-4). Suppose 3*i**5 - 21*i**4 - 5*i**3 - l*i**2 + 20*i**3 + 6*i**5 = 0. What is i?
0, 1/3, 1
Let r = 20689/48 + -431. Let s(d) be the second derivative of 0*d**2 - d + 1/80*d**5 + 0 + 0*d**3 - r*d**4. Suppose s(t) = 0. Calculate t.
0, 1
Determine n, given that 48*n - 25 + 11 - 23*n + 15*n**2 - 4 + 62*n = 0.
-6, 1/5
Suppose 6*c = 10*c - 40. Let k be (5 + 45/(-10))*8/c. Factor 0 - 4/5*l + 4/5*l**3 + 2/5*l**2 - k*l**4.
-2*l*(l - 2)*(l - 1)*(l + 1)/5
Suppose -5*n + 3*h + 30 = 0, 41 = -2*n + 6*n + h. Let b be (n/(-6))/((-2)/4). Factor -b*i**2 - 3 + 1 + 5.
-3*(i - 1)*(i + 1)
Suppose -4*k + 2 = 2*x - 4, 4*k - x - 21 = 0. Let c(i) be the second derivative of 0 + 6*i + 0*i**2 + 1/40*i**5 - 1/12*i**3 - 1/16*i**k. Solve c(w) = 0 for w.
-1/2, 0, 2
Let w(h) be the third derivative of 3*h**6/20 + 31*h**5/30 + 28*h**4/27 + 4*h**3/9 - 64*h**2. Determine t so that w(t) = 0.
-3, -2/9
Factor 96/5*u**2 + 14/3*u**4 + 0 - 2/5*u**5 - 88/5*u**3 + 128/15*u.
-2*u*(u - 4)**3*(3*u + 1)/15
Let y(l) be the third derivative of l**9/3780 + l**8/1120 - l**6/360 - l**4/2 + 4*l**2. Let z(p) be the second derivative of y(p). Factor z(c).
2*c*(c + 1)**2*(2*c - 1)
Suppose 4 + 11 = 5*x. Suppose -x*v - 154 = -490. Factor 5*r**2 - 121 + v + 16*r**2 + 12*r.
3*(r + 1)*(7*r - 3)
Let z = 284 - 131. Find i such that 580*i + 4*i**3 + z*i + 467*i - 1741 - 2259 - 120*i**2 = 0.
10
Suppose 8*s = 213 - 189. Solve 0 + 0*p + 0*p**4 + 0*p**2 - 4/9*p**5 + 0*p**s = 0 for p.
0
Let i(j) = 3*j**4 + 6*j**3 + 3*j**3 - 8*j**2 - 2*j + 8*j - 6 + 2*j**4. Let d(l) = 6*l**4 + 10*l**3 - 9*l**2 + 7*l - 7. Let p(u) = -6*d(u) + 7*i(u). Factor p(o).
-o**2*(o - 2)*(o - 1)
Let x(o) = 0*o + o + 9 - 21 + 2. Let s be x(12). Factor 5/4*j + 1/4*j**3 - 1/2 - j**s.
(j - 2)*(j - 1)**2/4
Let q(s) be the first derivative of 129*s**3 + 771*s**2/2 - 6*s + 761. Factor q(c).
3*(c + 2)*(129*c - 1)
Let m(f) be the second derivative of 5/6*f**3 + 0*f**2 + 0 + 0*f**6 - 29*f + 5/42*f**7 + 0*f**4 - 1/2*f**5. Factor m(v).
5*v*(v - 1)**2*(v + 1)**2
Factor -9680*q + 191 - 191 + 6*q**4 - q**4 + 9240*q**2 + 435*q**3.
5*q*(q - 1)*(q + 44)**2
Suppose -5*r + 25 = -5*j, -2*j - 2 = r - 1. Factor 2*y**2 + y**4 + y**r - 5*y**3 - 139 + 4*y + 136.
(y - 3)*(y - 1)**2*(y + 1)
Factor 69*g + 27*g**3 - 3/2*g**4 - 72*g**2 - 45/2.
-3*(g - 15)*(g - 1)**3/2
Let g(t) = 20*t - 140. Let r be g(7). Let f(x) be the second derivative of 0*x**2 + 0 + 7*x - 1/10*x**5 + r*x**3 + 1/12*x**4. Factor f(n).
-n**2*(2*n - 1)
Let h(i) be the third derivative of -i**8/1344 + 3*i**6/160 - 33*i**2 - i. Determine s so that h(s) = 0.
-3, 0, 3
Suppose h + 3*i + 4 = -3*h, -3*h - 5*i = 14. Let -7*w**3 + 5*w**4 + 30*w**h - 61*w**2 + 33*w**2 = 0. What is w?
0, 2/5, 1
Suppose -15*t = 4*t - 76. Let i(l) be the first derivative of -6/5*l**5 + 0*l + 15/8*l**t - l**3 + 1/4*l**6 + 0*l**2 + 1. Factor i(u).
3*u**2*(u - 2)*(u - 1)**2/2
Let b(a) = -a**2. Let c(t) = 3*t**2 + 8*t - 13. Let s(i) = -4*b(i) - c(i). Let y be s(7). Factor -3*r**3 - 2 + 3*r + 12 - y*r**2 - 4.
-3*(r - 1)*(r + 1)*(r + 2)
Let u(h) = -24*h + 173. Let i be u(7). Solve 3/2*o + 4*o**4 + 0*o**3 - 3/2*o**i - 5*o**2 + 1 = 0.
-1, -1/3, 1, 2
Let p(g) be the second derivative of -11/3*g**4 + 43*g + 0 - 4*g**3 - 2/15*g**6 + 0*g**2 - 6/5*g**5. What is h in p(h) = 0?
-3, -2, -1, 0
Suppose -5*c - 8*c = -3*c. Suppose c*q + 1/9 - 1/9*q**2 = 0. What is q?
-1, 1
Let d = -16 - -1. Let v be (6/(-15))/(3/d). Factor 2*p**v - 2*p - 2*p**2 - p**2 - 1.
-(p + 1)**2
Let g(c) be the third derivative of -c**6/840 - 13*c**5/420 - c**4/14 - 451*c**2. Factor g(x).
-x*(x + 1)*(x + 12)/7
Let x(s) be the third derivative of s**5/12 - 5*s**4/6 + 10*s**3/3 + 69*s**2 - s. Factor x(f).
5*(f - 2)**2
Let o(d) = 0*d + 6*d - 6 - 14*d. Let h be o(-1). Factor h*y + 1/4*y**2 + 4.
(y + 4)**2/4
Suppose -4*d + 48 = 5*z, -5*z - 66 + 12 = -2*d. Let c be 3 + d/(-5) + (-4)/(-10). Factor c + 3/2*m**3 - 1/2*m**4 + 0*m - m**2.
-m**2*(m - 2)*(m - 1)/2
Suppose 5*j + 2*a = 0, -4*a = -5*j + j. Let c be -2 - (8/44 - 138/33). Find k, given that 1/2*k**4 - 1/2*k**c + j + k - k**3 = 0.
-1, 0, 1, 2
Let k be (88/66)/(2 - 0). Let -k*b + 0*b**2 - 4/9 + 2/9*b**3 = 0. Calculate b.
-1, 2
Suppose 2 = 33*z - 32*z. Suppose 0 = -z*o - 4, 10*o + 10 = 2*u + 5*o. Factor -1/4*f + u + 0*f**4 + 1/2*f**3 + 0*f**2 - 1/4*f**5.
-f*(f - 1)**2*(f + 1)**2/4
Let k(a) be the third derivative of -a**8/2184 - 2*a**7/195 - 19*a**6/390 + 16*a**5/195 + 37*a**4/52 - 30*a**3/13 - a**2 - 58*a. Solve k(j) = 0 for j.
-10, -3, 1
Let o(d) be the second derivative of d**4/42 - 89*d**3/21 + 88*d**2/7 - 535*d. Factor o(z).
2*(z - 88)*(z - 1)/7
Let v = -92 + 95. Determine c, given that 12*c**3 + 2*c**2 + 10*c**4 - v*c**5 - 26*c**2 - 4*c**4 = 0.
-2, 0, 2
Find j, given that -j**2 - 1/2*j**3 + 0 + 4*j = 0.
-4, 0, 2
Let q(h) = 9*h**2 - 2*h + 2. Let l be q(1). Suppose 0 = -l*z + 13*z - 8. Suppose -36*a**2 - 2*a**3 + 27*a - 2*a**3 - 4 + 19*a**3 - z = 0. What is a?
2/5, 1
Let o be -20 + 1 + 123471/6456. Factor -1/8*y**2 - 1/8*y**3 + 0 + 0*y + o*y**4