3/15
Let t(n) be the third derivative of -3*n**5/80 + n**4/16 - n**3/24 - n**2 - 23*n. Suppose t(i) = 0. What is i?
1/3
Let d(o) be the second derivative of o**6/80 + o**5/20 + o**4/16 + 10*o**2 + 31*o. Let f(l) be the first derivative of d(l). Factor f(j).
3*j*(j + 1)**2/2
Let q(y) = 26*y**3 - 118*y**2 + 224*y - 130. Let m(j) = -j**4 - 52*j**3 + 235*j**2 - 448*j + 261. Let i(a) = -2*m(a) - 5*q(a). Determine o, given that i(o) = 0.
1, 4
Let x(f) = 37*f**3 + 270*f**2 + 887*f + 776. Let q(a) = -12*a**3 - 90*a**2 - 296*a - 258. Let h(d) = -13*q(d) - 4*x(d). Suppose h(p) = 0. Calculate p.
-5, -5/4
Let i(p) be the second derivative of -p**6/540 - p**5/180 + p**3/3 + 3*p. Let n(x) be the second derivative of i(x). Factor n(b).
-2*b*(b + 1)/3
Let p(t) be the first derivative of -t**8/420 + 7*t**6/90 + t**5/5 + 4*t**3/3 + 11. Let v(s) be the third derivative of p(s). Find a, given that v(a) = 0.
-2, -1, 0, 3
Let r(p) be the first derivative of p**4/16 + p**3/6 - p**2/8 - p/2 + 107. Factor r(s).
(s - 1)*(s + 1)*(s + 2)/4
Let u = 313 - 308. Let x(q) be the third derivative of 0 + q**2 - 1/270*q**u + 0*q + 1/27*q**3 + 1/36*q**4 - 1/180*q**6. What is j in x(j) = 0?
-1, -1/3, 1
Suppose 1/11*t**2 + 20/11*t - 21/11 = 0. What is t?
-21, 1
Suppose -4/9*i + 0 - 118/9*i**2 = 0. Calculate i.
-2/59, 0
Suppose -7*o = o - 24. Factor -x**3 + 4*x**o - 8*x**3 - 5*x**4.
-5*x**3*(x + 1)
Suppose -6*h + h = -160. Suppose 2*z + 0*z - h = 0. Let -z - 2*b**3 + 3*b + 14 + b**3 = 0. Calculate b.
-2, 1
Let v = -27 + 29. Suppose -v*w = w - 5*s - 45, -s = -w + 13. Let t(c) = -c**2. Let y(o) = -o**3 - 6*o**2. Let f(m) = w*t(m) - 2*y(m). Let f(l) = 0. What is l?
-1, 0
Let k be -1*(-3)/(-13 - -10) + (5 - -1). Find w, given that -8/15*w**3 + 0*w - 2/15*w**k + 0 + 0*w**2 + 2/3*w**4 = 0.
0, 1, 4
Let y(k) be the second derivative of -k**6/540 - k**5/90 - k**4/36 - k**3/27 + 11*k**2/2 - 35*k. Let a(p) be the first derivative of y(p). Factor a(r).
-2*(r + 1)**3/9
Let n(f) be the second derivative of 0*f**2 + 1/2*f**3 - 6*f - 3/20*f**5 + 0 + f**4 - 2/5*f**6. Factor n(y).
-3*y*(y - 1)*(y + 1)*(4*y + 1)
Suppose -5*a + 2*m = -2, -3*m = 3*a + 2*m + 5. Suppose -u + a = -0. Factor 0*z - 1/5*z**2 + 1/5*z**4 + u + 0*z**3.
z**2*(z - 1)*(z + 1)/5
Let p be 1/28*(9 + (-135)/27). Determine x, given that -4/7 - 4/7*x + p*x**2 + 1/7*x**3 = 0.
-2, -1, 2
Suppose 10/3 - 20/3*q**2 + 10/3*q**4 - 5/3*q - 5/3*q**5 + 10/3*q**3 = 0. Calculate q.
-1, 1, 2
Let v(j) = j**2 + j - 1. Let r(n) = -9*n**2 - 9*n + 13. Let d(i) = i + 5. Let c be d(-6). Let f(h) = c*r(h) - 5*v(h). Solve f(l) = 0 for l.
-2, 1
Let v(q) be the first derivative of q**8/112 - 3*q**6/40 + q**5/10 + 14*q**2 + 10. Let n(g) be the second derivative of v(g). Factor n(c).
3*c**2*(c - 1)**2*(c + 2)
Let q = -67 - -70. Determine v so that 9*v + 0*v + v**3 - 2*v**4 - 3*v + 2*v**2 - 7*v**q = 0.
-3, -1, 0, 1
Let f(h) be the third derivative of 0*h - 4*h**3 - 11/4*h**4 + 1/14*h**7 + 3/20*h**5 + 11/20*h**6 - 11*h**2 + 0. Suppose f(x) = 0. What is x?
-4, -1, -2/5, 1
Let i(g) be the first derivative of g**6/165 - g**4/11 - 8*g**3/33 - 3*g**2/11 - 28*g + 40. Let t(n) be the first derivative of i(n). Factor t(f).
2*(f - 3)*(f + 1)**3/11
Let s(h) be the first derivative of -7*h**4/18 + 32*h**3/27 - 11*h**2/9 + 4*h/9 - 55. Factor s(g).
-2*(g - 1)**2*(7*g - 2)/9
Let n = -1155 - -1158. Factor -4/13*f**2 + 0 - 2/13*f**n - 2/13*f.
-2*f*(f + 1)**2/13
Let k(p) be the third derivative of p**7/350 + p**6/200 - 3*p**5/100 - p**4/40 + p**3/5 + 129*p**2 + 1. Factor k(j).
3*(j - 1)**2*(j + 1)*(j + 2)/5
Suppose -x = 4*x, 5*x - 3 = -g. Suppose -3*b**3 + b**g + 2*b**2 + 0*b**2 + 0*b**3 = 0. Calculate b.
0, 1
Suppose -1/3*o**4 - 2*o**2 - 4/3*o + 5/3*o**3 + 8/3 = 0. Calculate o.
-1, 2
Solve -3/4*l - 1/2*l**2 + 1/4*l**5 + 1/2*l**3 + 3/4*l**4 - 1/4 = 0 for l.
-1, 1
Suppose -r - 2*n + 7*n = 21, -5*r + 40 = 4*n. Factor -8*g**r + 3*g**4 + 2*g**3 + 2*g**4 + g**5.
g**3*(g - 2)*(g - 1)
Let l = 22 - 13. Let t(b) = -b**3 + 8*b**2 + 8*b + 9. Let p be t(l). Factor -g**3 + 0*g**4 + 1/2*g + 0*g**2 + 1/2*g**5 + p.
g*(g - 1)**2*(g + 1)**2/2
Factor 251*o**3 + 34*o + 16*o**2 - 249*o**3 + 0 + 20.
2*(o + 1)*(o + 2)*(o + 5)
Let o = 116 - 114. Factor 40*y**2 - 3*y**3 + 42*y**2 - 6*y - 73*y**o.
-3*y*(y - 2)*(y - 1)
Let u(k) be the first derivative of 3/2*k**2 - 43 + 0*k + 1/3*k**3. Factor u(l).
l*(l + 3)
Factor -1/2*i**2 + 1/6*i**3 - 14/3*i + 0.
i*(i - 7)*(i + 4)/6
Let g(r) be the second derivative of r**5/100 - 11*r**4/60 + 7*r**3/6 - 5*r**2/2 + 14*r - 2. Factor g(c).
(c - 5)**2*(c - 1)/5
Determine c, given that -1/6*c**4 + 1/3*c**3 - 3*c - 9/2 + 2*c**2 = 0.
-3, -1, 3
Suppose -4*l = -5*q - 0*l - 27, 3*q - l + 19 = 0. Let b = q - -11. Solve 2/9*o**2 + 2/9*o**5 + 0 - 2/9*o**b + 0*o - 2/9*o**3 = 0 for o.
-1, 0, 1
Let s(i) = -2*i**4 - 5*i**3 + 4*i**2 + 3. Let n(c) = -c**4 - 2*c**3 + 2*c**2 + 1. Let b(t) = -5*n(t) + 2*s(t). Find v, given that b(v) = 0.
-1, 1
Suppose 5*a + j + 4 = 0, 37 = -3*a + 3*j + 49. Let s(q) be the third derivative of a + 2*q**2 + 0*q**3 + 0*q + 0*q**4 + 1/60*q**5. Suppose s(i) = 0. What is i?
0
Let w(a) be the second derivative of a**5/30 - a**4/12 - 13*a**2/2 - 18*a. Let o(k) be the first derivative of w(k). Solve o(q) = 0.
0, 1
Let k(n) = -n**2 + 16*n - 44. Let l be k(4). Let t(a) be the second derivative of 0 - 4*a + 0*a**3 + 0*a**l - 1/10*a**5 + 0*a**2. Solve t(z) = 0.
0
Suppose -u = i - 26 + 10, -41 = -i + 4*u. Let t = i - 187/9. Solve -2/3*l - 2 - t*l**3 + 10/9*l**2 = 0.
-1, 3
Factor -15*v**2 + 15 + 1/2*v**3 - 1/2*v.
(v - 30)*(v - 1)*(v + 1)/2
Let u(m) be the first derivative of 4/3*m**2 - 2/45*m**3 - 40/3*m + 33. Factor u(w).
-2*(w - 10)**2/15
Let k(p) be the second derivative of p**7/315 + 4*p**6/225 + p**5/25 + 2*p**4/45 + p**3/45 - 115*p. Solve k(a) = 0.
-1, 0
Let x(l) be the third derivative of -l**7/630 - l**6/72 + l**5/30 + 4*l**4/9 - 16*l**3/9 - 56*l**2. Let x(j) = 0. Calculate j.
-4, 1, 2
Let z(x) be the first derivative of -2662*x**6/3 - 484*x**5 + 594*x**4 - 496*x**3/3 + 16*x**2 + 165. Suppose z(g) = 0. What is g?
-1, 0, 2/11
Suppose 16*q - 76 = -12. Factor -3/4 + 3/2*l**2 - 3/4*l**5 + 3/2*l**3 - 3/4*l - 3/4*l**q.
-3*(l - 1)**2*(l + 1)**3/4
Factor 37*p**3 + 15*p**3 - 18*p + 69*p**2 + 2*p**4 + 0*p**4 + 7*p**4.
p*(p + 3)**2*(9*p - 2)
Solve 6/5*r**4 + 9/5*r**5 + 6/5 - 18/5*r**3 - 12/5*r**2 + 9/5*r = 0 for r.
-1, -2/3, 1
Suppose -9 = -7*t + 5. Let -6*q + 37*q - 6*q**t - 15*q + 6 = 0. What is q?
-1/3, 3
Let u(x) be the first derivative of -2*x**5/55 - 6*x**4/11 - 2*x**3/3 - 1. Find q such that u(q) = 0.
-11, -1, 0
Let v(l) be the second derivative of -3*l**5/40 + l**4/2 - l**3/4 - 9*l**2/2 + 23*l. Determine t, given that v(t) = 0.
-1, 2, 3
Suppose 2*t = -6, 5 = 29*o - 28*o - t. Let m(d) be the first derivative of 0*d**o + 1/20*d**5 + 1/12*d**3 + 0*d + 1/8*d**4 - 9. Solve m(z) = 0.
-1, 0
Suppose -d = 2*d - 6. Suppose a - 3*w = -6, -d*a + a - 9 = -4*w. Factor a*o**2 - 4*o**2 - 5 + 1 - 6*o - 5.
-(o + 3)**2
Suppose -3*w + 4*m + m = -12, -4*w = -4*m - 16. Suppose 18*g**2 + 22*g**3 + 0*g**w - 2*g**2 - 4*g - 6*g**2 + 8*g**4 = 0. Calculate g.
-2, -1, 0, 1/4
Let s(h) be the first derivative of -h**5/210 - 5*h**4/84 - 2*h**3/7 - 2*h**2 + 8. Let f(a) be the second derivative of s(a). Determine v, given that f(v) = 0.
-3, -2
Let r = -1 - -4. Let g = 1193 - 1191. Factor 0 + 0*w + 1/4*w**r - 1/4*w**g.
w**2*(w - 1)/4
Let p(t) = 6*t**2. Let h(r) = -r**2. Let q(d) = d**3 - 6*d**2 + 8*d - 7. Let y be -9 + 8 - 6/(-1). Let g be q(y). Let u(j) = g*h(j) + p(j). Factor u(i).
-2*i**2
Let u(q) be the second derivative of q**6/15 - 12*q**5/5 + 143*q**4/6 + 8*q**3 - 144*q**2 + 2*q + 8. Find h such that u(h) = 0.
-1, 1, 12
Let o be 29/28 + (-2604)/196 + 13. Factor -3/4*l**4 + 3/4*l + 0 + 3/4*l**2 - o*l**3.
-3*l*(l - 1)*(l + 1)**2/4
Let b(m) be the third derivative of -m**5/105 + 10*m**4/21 - 128*m**3/21 + 301*m**2. Solve b(v) = 0.
4, 16
Let d(x) be the third derivative of -x**7/4620 + x**5/660 - 2*x**3/3 - 6*x**2. Let j(k) be the first derivative of d(k). Solve j(a) = 0.
-1, 0, 1
Let j(l) be the first derivative of l**6/510 + l**5/510 - l**4/204 - 5*l**2 - 3. Let m(w) be the second derivative of j(w). Let m(q) = 0. Calculate q.
-1, 0, 1/2
Suppose 2/9*i**3 + 10/9*i + 16/9*i**2 - 28/9 = 0. Calculate