. What is l?
1, 2
Let h(r) be the second derivative of -2/3*r**3 + r + 0 + 0*r**2 - 1/5*r**5 + 2/3*r**4. Find a such that h(a) = 0.
0, 1
Let g(f) be the first derivative of -3 + 0*f**2 - 3/20*f**4 - 1/15*f**3 - 1/30*f**6 - 3/25*f**5 + 0*f. Factor g(m).
-m**2*(m + 1)**3/5
Let i = 1800/6251 + -2/893. Factor 2/7*q**3 + i*q - 4/7*q**2 + 0.
2*q*(q - 1)**2/7
Let b(p) = 3*p**2 + 8*p + 25. Let q(c) = -c**2 + c. Let k(o) = b(o) + 2*q(o). Solve k(j) = 0.
-5
Let i(a) = a. Let k be i(2). Find s such that 0*s**3 - 3*s**3 - 2*s**k - 2*s**2 + 5*s**3 = 0.
0, 2
Suppose 3*k = 6, 3*y - 7*y = -k + 46. Let x(b) = 60*b**2 + 14*b - 21. Let z(g) = 12*g**2 + 3*g - 4. Let a(n) = y*z(n) + 2*x(n). Solve a(d) = 0 for d.
-2/3, 1/4
Let d be -1 + (3 - 4) + -1. Let c = 5 + d. Determine r so that -r**2 - 4*r**c - r + 4*r**2 = 0.
-1, 0
Let i(m) be the first derivative of m**2 - 5*m**2 + 3*m**3 - 2*m**3 - 5*m**3 - m**4 + 3. Determine c so that i(c) = 0.
-2, -1, 0
Let y(p) = -9*p**2 + 6*p - 21. Let t(u) = -u**2 - 1. Let o(f) = -12*t(f) + y(f). Let o(n) = 0. What is n?
-3, 1
Let b = -7 + 12. Solve 4*k**4 - 4*k**2 + 6*k**3 - 4*k**4 + 7*k**b - 9*k**5 = 0.
-2, 0, 1
Let m = -3687593 + 6652418111/1804. Let z = -1/164 + m. Factor z + 0*c - 2/11*c**2.
-2*(c - 1)*(c + 1)/11
Let n(u) be the first derivative of -4*u**3/21 + 6*u**2/7 - 8*u/7 + 47. Suppose n(z) = 0. Calculate z.
1, 2
Let k(i) = -i**2 + 9*i + 0 + 0*i**2 - 2. Let w be k(8). Let q**2 + 6*q**4 - 3*q**3 + q**5 - 3*q**4 + w*q**3 = 0. What is q?
-1, 0
Let z(s) be the third derivative of -1/360*s**5 + 2*s**2 + 1/24*s**4 - 1/4*s**3 + 0*s + 0. Let z(f) = 0. Calculate f.
3
Factor 3*l - 5*l + 3*l + 2*l**2 + l**3.
l*(l + 1)**2
Let m be (-1 - 6) + (-16)/(-4). Let w be (-20)/6*m/15. Factor -w*x**2 + 0*x + 0 + 2/3*x**3 + 2/3*x**4 - 2/3*x**5.
-2*x**2*(x - 1)**2*(x + 1)/3
Suppose -r + 2*r - 14 = 3*h, -4*r - h = -4. Let f(b) be the first derivative of -r - 4/7*b**3 - 6/35*b**5 + 0*b**2 + 4/7*b**4 + 2/7*b. Solve f(m) = 0.
-1/3, 1
Let x(f) be the third derivative of 0 + 0*f**3 + 0*f**5 + 1/560*f**8 + 0*f + f**2 + 0*f**7 - 1/200*f**6 + 0*f**4. Determine j so that x(j) = 0.
-1, 0, 1
Suppose -2*a + 16 = -4*x, -16 = x + 3*x. Suppose -2*o + 5 = b, -5*o = 4*b - a*b - 20. Factor o*z**3 + 0*z - 1/2*z**2 + 1/4*z**4 + 1/4.
(z - 1)**2*(z + 1)**2/4
Let t(k) be the first derivative of 2*k**2 - k**4 - 5 + 4*k - 4/3*k**3. Let t(v) = 0. What is v?
-1, 1
Let k(s) be the first derivative of -s**7/735 - s**6/210 + s**4/42 + s**3/21 + s**2/2 - 4. Let i(z) be the second derivative of k(z). Factor i(m).
-2*(m - 1)*(m + 1)**3/7
Suppose 2*q - z = q + 5, 0 = -5*z. Let 6*r**2 - q*r**2 + r**2 = 0. Calculate r.
0
Solve -1/3*j + 0 + 4/9*j**5 - 13/9*j**2 - 1/9*j**3 + 13/9*j**4 = 0.
-3, -1, -1/4, 0, 1
Let r be -1*2/(-8)*9. Factor 15/2*h - 25/4*h**2 - r.
-(5*h - 3)**2/4
Let u(p) be the first derivative of -p**6/2 + 9*p**5/5 - 9*p**4/4 + p**3 + 4. Find q such that u(q) = 0.
0, 1
Let s = 11 - 7. Suppose s*q**2 + 0*q**2 - 11*q**3 + 2*q**4 + 5*q**3 = 0. What is q?
0, 1, 2
Factor 0 - 69/2*r**4 + 3*r + 81/2*r**3 + 21/2*r**5 - 39/2*r**2.
3*r*(r - 1)**3*(7*r - 2)/2
Factor -9*h**3 - 3 + 9*h - 2*h**2 + 4*h**2 + h**2.
-3*(h - 1)*(h + 1)*(3*h - 1)
Let f be (0 - -7) + -10 - 102/(-30). Solve 2/5*a**5 + 0 - 6/5*a**3 - 4/5*a + f*a**4 - 2*a**2 = 0.
-1, 0, 2
Let f = 18 + -16. Suppose -2*q**f - 4*q + 0*q + q**3 + 4*q = 0. Calculate q.
0, 2
Suppose -3*n = n - 12. Factor -4 + j - n*j**4 - 5*j**3 + 5*j + 7 - j**3.
-3*(j - 1)*(j + 1)**3
Let j(o) be the first derivative of -o**6/1080 + o**5/360 + o**4/36 + o**3 + 4. Let d(l) be the third derivative of j(l). Factor d(z).
-(z - 2)*(z + 1)/3
Let t(x) be the first derivative of -4*x**5/3 - 35*x**4/12 - 10*x**3/9 + 5*x**2/6 - 1. Solve t(w) = 0 for w.
-1, 0, 1/4
Let k(j) be the third derivative of 3*j**2 + 0*j + 0*j**3 + 0 + 1/24*j**4 - 7/120*j**5. Suppose k(o) = 0. Calculate o.
0, 2/7
Factor -270*y**2 + 48*y**3 - 5*y**4 - 158*y + 377*y + 381*y - 375 + 2*y**4.
-3*(y - 5)**3*(y - 1)
Suppose -1/5*t**3 - 1/5*t**2 + 2/5*t + 0 = 0. What is t?
-2, 0, 1
Suppose 4*x = 3*s - 1, s - 4*s + 17 = 4*x. Let k be x/(-3 + 11 - 0). Determine g, given that 1/4*g - g**4 - k*g**3 + 0 + g**2 = 0.
-1, -1/4, 0, 1
Let b(n) = -n**2 + 1. Let q(d) = -10*d**2 + 10. Let k(l) = -35*b(l) + 4*q(l). Factor k(m).
-5*(m - 1)*(m + 1)
Let v(w) be the first derivative of -3*w**5/20 + 3*w**4/16 + w**3/4 - 3*w**2/8 + 25. Factor v(n).
-3*n*(n - 1)**2*(n + 1)/4
Suppose -2*j + 1 + 5 = 0. Suppose 3*m + 4*y - 17 = 0, 5 = j*y - 1. Solve 0*z**2 + 0 + 2/9*z**4 + 0*z - 2/9*z**m + 4/9*z**5 = 0.
-1, 0, 1/2
Let f = 4 - 1. Let z(n) = -5*n**4 + 0*n**f + 9*n**2 - 7 + 9*n**3 - 2*n**2. Let x(p) = -3*p**4 + 5*p**3 + 4*p**2 - 4. Let y(r) = 7*x(r) - 4*z(r). Factor y(j).
-j**3*(j + 1)
Suppose 29*c + 30 = 44*c. Let u be 1/(-3) - (-22)/30. Find n such that -2/5 + 0*n + u*n**c = 0.
-1, 1
Solve -2/9*q**4 + 2/9 + 4/9*q + 0*q**2 - 4/9*q**3 = 0.
-1, 1
Suppose -3/4*r**2 - 192 - 24*r = 0. Calculate r.
-16
Let 8/3*i - 2/3*i**3 - 2/3*i**2 + 8/3 = 0. Calculate i.
-2, -1, 2
Let j(c) be the second derivative of c**7/2940 + c**6/630 + c**5/420 + c**3/2 - 4*c. Let m(u) be the second derivative of j(u). Let m(y) = 0. What is y?
-1, 0
Let d(r) be the third derivative of -r**5/12 - 5*r**4/8 + 10*r**3/3 - 9*r**2. What is y in d(y) = 0?
-4, 1
Let a(h) be the second derivative of -h**7/420 - h**6/135 - h**5/180 + 2*h**3/3 + 6*h. Let q(v) be the second derivative of a(v). Factor q(d).
-2*d*(d + 1)*(3*d + 1)/3
Let i(s) be the second derivative of s**7/840 - s**6/120 - s**4/4 + 4*s. Let h(b) be the third derivative of i(b). Let h(l) = 0. Calculate l.
0, 2
Suppose 6 = -3*r + r. Let z(n) = -n**2 + n + 3. Let k(h) = 2. Let v(s) = r*k(s) + 2*z(s). What is f in v(f) = 0?
0, 1
Let f = 8/21 - -4/21. Solve -f*r**2 - 2/7*r**4 + 0 + 0*r + 6/7*r**3 = 0.
0, 1, 2
Let a = 59870/3 - 400790/21. Let q = a + -870. Let -q*s + 8/7*s**2 + 2/7 = 0. What is s?
1/4, 1
Let l(d) be the second derivative of 0 + 1/4*d**3 - 6*d - 1/6*d**2 + 1/24*d**5 - 1/6*d**4. Determine r so that l(r) = 0.
2/5, 1
Let n = 51 + -50. Let y(j) be the first derivative of 0*j**2 + 0*j + 2/3*j**3 + 1/5*j**5 - n + 3/4*j**4. Determine c so that y(c) = 0.
-2, -1, 0
Solve 2 - 6*m - 12*m + 1 - 9*m**2 + 24*m**2 = 0 for m.
1/5, 1
Let s(q) = -q**2 + 6*q - 4. Let y be s(5). Let h(x) = 3*x - 1. Let w be h(y). Factor -2*c**2 + 2*c**2 + 2*c**w.
2*c**2
Factor -8/15*m - 4/5*m**2 - 2/15 - 8/15*m**3 - 2/15*m**4.
-2*(m + 1)**4/15
Let s(c) = 10*c + 87*c + 17*c**2 - 1 - 252*c**2 - 2*c. Let i(u) = -118*u**2 + 47*u - 1. Let z(t) = -7*i(t) + 3*s(t). Find f, given that z(f) = 0.
2/11
Let u(n) be the first derivative of -1/3*n**3 + n**2 - 1 + 0*n. Factor u(y).
-y*(y - 2)
Factor -g**2 - 128*g - 2*g**2 + 7*g**2 + 1024.
4*(g - 16)**2
Let u(h) = h**2 + 5*h. Let k(j) = j - 1. Let g be k(-4). Let t be u(g). Solve -f**3 + 1/2*f**4 + t + 1/2*f**2 + 0*f = 0.
0, 1
Factor 2/11*h**4 - 2/11*h**5 + 2/11 - 4/11*h**2 + 4/11*h**3 - 2/11*h.
-2*(h - 1)**3*(h + 1)**2/11
Suppose 9*u + 12*u = 42. Factor -4 - 1/4*s**u - 2*s.
-(s + 4)**2/4
Suppose 0 = 3*b + 5*l - 3, -2*b + 5*l = -0*b - 2. Let w be (b - 3) + (1 - -6). Factor 10*g - 2*g**2 + w*g**2 - 7*g.
3*g*(g + 1)
Let u be 9/(-18)*(-3 + 0). Factor 0*b + 0 - u*b**3 - 3/2*b**2.
-3*b**2*(b + 1)/2
Suppose -5*s = -12*s + 42. Let c(h) be the third derivative of 0 - 1/6*h**3 + 7/48*h**4 + 1/60*h**5 + 0*h - 7/240*h**s + 2*h**2. Let c(w) = 0. What is w?
-1, 2/7, 1
Let t = 51/236 + 2/59. Factor -1/2*p**2 + 1/2 + p**3 + 0*p**4 - 3/4*p - t*p**5.
-(p - 1)**3*(p + 1)*(p + 2)/4
Let z = -49 - -99. Factor 5*i**2 + 4*i**2 + z + 27*i - 23 + i**3.
(i + 3)**3
Let p be 2/7*(-1 - -15). Let 3*o**3 + 1 - o**2 + 5*o**3 - p*o**3 + 0*o - 4*o = 0. Calculate o.
-1, 1/4, 1
Let z(h) be the third derivative of h**7/1050 + h**6/600 - h**5/150 + 40*h**2. Factor z(u).
u**2*(u - 1)*(u + 2)/5
Let t(u) be the second derivative of 3*u**5/20 + u**4/2 + 6*u. Solve t(p) = 0.
-2, 0
Let g(v) be the third derivative of -2*v**5/15 + 5*v**4/4 + 4*v**3/3 + 8*v**2. Factor g(i).
-2*(i - 4)*(4*i + 1)
Let b(u) be the third derivative of 1/672*u**8 + 0*u + 0*u**3 + 0*u**4 - 3*u**2 + 1/80*u**6 + 0 - 1/120*u**5 - 1/140*u**7. Let b(w) = 0. What is w?
0, 1
Let n(m) = -m**2 + 3. Let r be n(0). Suppose 0*u - 7*u + 21 = 0. Factor a**5 - 3*a**3