- 2/3*r**3 - 2/9*r**j - 2/9*r**5 = 0. Calculate r.
-1, 0
Let y(a) be the second derivative of a**6/540 - a**5/270 - a**4/54 - 2*a**2 - 8*a. Let z(v) be the first derivative of y(v). Let z(o) = 0. What is o?
-1, 0, 2
Let b(t) be the third derivative of 0*t - 1/10*t**5 - 3/32*t**4 - 5*t**2 + 0 - 1/24*t**3 - 1/30*t**6. Factor b(y).
-(y + 1)*(4*y + 1)**2/4
Let h(o) = 4*o**2 - o - 5. Let b(l) = -l**3 - l**2 + l + 1. Let y be 3/(-6) + 2/(-4). Let g(k) = y*h(k) - 4*b(k). Determine z so that g(z) = 0.
-1, 1/2
Factor 0 + 2/25*o**4 + 12/25*o**3 + 0*o + 18/25*o**2.
2*o**2*(o + 3)**2/25
Let y be -3*28/90*(-18)/21. Suppose -4*p = -2*p - 8, -2*q = 5*p - 30. Solve y*l**2 + 2*l**3 + 8/5*l**4 + 2/5*l**q + 0*l + 0 = 0.
-2, -1, 0
Let m(o) = o - 8. Let c be m(12). Suppose -c*p + 9 = -p. Factor 12*q**2 - 2*q - 10*q**3 - 2*q**5 - q**5 - 14*q**3 + 20*q**4 - p*q**5.
-2*q*(q - 1)**3*(3*q - 1)
Let d(l) = 2*l + 9. Let w be d(0). Suppose -5*y = 4*g - 7, -y + 0*g = -3*g - w. Factor 8*p**2 - 54*p**5 - 2/3*p - 36*p**y + 72*p**4 + 0.
-2*p*(3*p - 1)**4/3
Let j(u) be the first derivative of 0*u + 4/3*u**3 + u**2 + 3 + 1/2*u**4. Let j(a) = 0. Calculate a.
-1, 0
Let c(j) be the third derivative of j**6/300 - j**4/20 - 2*j**3/15 + 7*j**2. Factor c(f).
2*(f - 2)*(f + 1)**2/5
Let h(v) be the third derivative of -v**6/300 + 2*v**5/75 - v**4/15 - 39*v**2. Suppose h(r) = 0. Calculate r.
0, 2
Let l = -1054 - -28462/27. Let k(f) be the first derivative of 1/27*f**6 + 1 - 1/9*f**4 + l*f**3 + 1/9*f**2 - 2/45*f**5 - 2/9*f. Factor k(z).
2*(z - 1)**3*(z + 1)**2/9
Suppose -o + 7 = s, 4*s + 0*s - 30 = -5*o. Find m, given that -8/9*m**4 - 2/9*m - 4/9 + 8/9*m**3 - 2/3*m**5 + 4/3*m**o = 0.
-1, 2/3, 1
Let b = 0 + 0. Let o be (2 + b)/(-2 + 3). Factor v**o - 2*v**2 + v - v.
-v**2
Suppose 6 = -4*x + 2, 4*t - x = 837. Let d = t - 1459/7. Factor -d - 2/7*w**2 + 6/7*w.
-2*(w - 2)*(w - 1)/7
Suppose -6*j + 25 = -j. Let w(i) be the third derivative of -1/84*i**4 + 1/35*i**j + 0*i**3 + 0 + 4/735*i**7 + 0*i - 3/140*i**6 - 2*i**2. Factor w(d).
2*d*(d - 1)**2*(4*d - 1)/7
Let y(k) = -18*k**5 - 13*k**4 - k**3 + 3*k**2 - 3*k - 3. Let r(u) = -37*u**5 - 25*u**4 - u**3 + 7*u**2 - 7*u - 7. Let b(v) = 3*r(v) - 7*y(v). Factor b(g).
g**3*(3*g + 2)*(5*g + 2)
Suppose 4*q = -3*q + 28. Let d = 6 - q. Let 2/7*f**3 + 2/7*f + 0 - 4/7*f**d = 0. What is f?
0, 1
Let k(z) be the first derivative of -2*z - 4 - 2*z**3 + 4*z**3 - 2*z**2 + 4*z**2. Let k(w) = 0. Calculate w.
-1, 1/3
Let j = -15 - -46/3. Let o(k) be the first derivative of 1 + k + j*k**3 - k**2. Factor o(h).
(h - 1)**2
Let o = 37/33 - 5/11. Let o - 1/3*w**2 + 1/3*w = 0. What is w?
-1, 2
Let j(y) be the first derivative of y**6/36 + y**5/15 - y**4/12 - 4*y**3/9 - 7*y**2/12 - y/3 - 7. Find a such that j(a) = 0.
-1, 2
Let t(c) be the third derivative of c**2 + 0 + 0*c**5 - 1/30*c**6 + 0*c - 1/3*c**3 + 1/6*c**4 + 1/105*c**7. Factor t(m).
2*(m - 1)**3*(m + 1)
Let x(l) be the third derivative of -2*l**2 + 5/12*l**4 + 0 + 0*l + 1/10*l**5 + 2/3*l**3. Suppose x(f) = 0. Calculate f.
-1, -2/3
Factor 1/5*r**2 + 6/5 + r.
(r + 2)*(r + 3)/5
Let d be 7/((-14)/(-4))*1. Let h(z) = 2*z**5 - 3*z**3 + 2*z**2 - 3*z. Let x(u) = u**5 + u**4 + u**2 - u. Let a(v) = d*h(v) - 6*x(v). Factor a(i).
-2*i**2*(i + 1)**3
Determine r, given that 3/2*r + 3/2*r**5 - 3*r**2 + 3/2 + 3/2*r**4 - 3*r**3 = 0.
-1, 1
Let r(l) be the second derivative of 0 - 4/13*l**4 - 3/13*l**3 + l - 11/65*l**5 - 1/273*l**7 - 8/195*l**6 + 0*l**2. Factor r(i).
-2*i*(i + 1)**2*(i + 3)**2/13
Let n = 16 - 8. Suppose -2*w = -6*w + n. Determine o so that -2*o**w + 8*o**2 - 2*o**2 - o**2 = 0.
0
Let h = 0 + 3. Factor -4 + i**h + i**2 + 0 + 4.
i**2*(i + 1)
Let m(z) be the first derivative of -z**3/2 + 3*z**2/2 - 3*z/2 - 30. Factor m(a).
-3*(a - 1)**2/2
Let q(h) be the first derivative of -1/11*h**2 - 4 + 0*h + 8/55*h**5 - 1/11*h**4 + 1/11*h**6 - 8/33*h**3. Let q(r) = 0. Calculate r.
-1, -1/3, 0, 1
Let c be (5 - (-105)/(-18))/(20/(-36)). Let z(l) be the second derivative of c*l**2 - 2*l + 1/4*l**4 + 0 + l**3. Factor z(r).
3*(r + 1)**2
Solve -8/3*i + 8 - 38/3*i**2 - 2*i**3 = 0.
-6, -1, 2/3
Let o be (1 + -7)/((-6)/9). Let w = o + -6. Factor -2*k**2 - 2*k - 4*k**w + 2*k**3 - 2*k**2.
-2*k*(k + 1)**2
Let p = 6 - -1. Factor -7*j**4 - 2*j**3 + 0*j**2 + p*j**2 + 4*j**3 - 2*j.
-j*(j - 1)*(j + 1)*(7*j - 2)
Let d(c) = -c**3 + c**2 + c + 1. Let l(g) = -16*g**3 - 52*g**2 - 296*g - 380. Let j(r) = -12*d(r) + l(r). What is w in j(w) = 0?
-7, -2
What is y in -3*y - 12*y + 16*y**2 - 4*y**3 + y + 2*y = 0?
0, 1, 3
Suppose 0 = -8*w + 7*w. Let m(a) be the second derivative of 0 + 1/6*a**4 + a + 0*a**2 - 1/10*a**5 + w*a**3. Suppose m(v) = 0. Calculate v.
0, 1
Let z be (-88)/(-32) + (0 - (-3)/12). Let o be -2*1 + -1 + 3. Factor 1/2*y**z + 0 + 0*y + o*y**2.
y**3/2
Let s = -14 - -17. Find f such that -5/2*f**4 - 5*f**s - 5/2*f - 1/2 - 1/2*f**5 - 5*f**2 = 0.
-1
Let o be ((-11)/(-22))/((-2)/(-5)). What is j in -o*j - 1/2 - j**2 - 1/4*j**3 = 0?
-2, -1
Suppose -5*d + 6 = -2*d. Factor 4 + 17*o**d + o - 12*o**2 + 11*o.
(o + 2)*(5*o + 2)
Let k = -2555/18 + 142. Let x(o) be the first derivative of 4/9*o**3 + 1/2*o**4 + 2 + 0*o + k*o**6 + 1/6*o**2 + 4/15*o**5. Factor x(c).
c*(c + 1)**4/3
Let j(v) = -4*v**3 + 2*v**2 + 2*v. Let s(x) = -x**3 - 4*x**2 + 1. Let k be s(-4). Let c(d) = d**3 - d**2 - d. Let b(h) = k*j(h) + 2*c(h). Factor b(l).
-2*l**3
Let c(f) be the second derivative of f**4/24 + 2*f. Solve c(s) = 0 for s.
0
Let j(u) be the second derivative of 32*u**7/7 - 64*u**6/15 - 17*u**5/5 + u**4/6 + u**3/3 - 39*u. What is d in j(d) = 0?
-1/4, 0, 1/6, 1
Let k(m) be the first derivative of -m**7/840 - m**6/120 - m**5/40 - m**4/24 + 2*m**3/3 - 2. Let z(f) be the third derivative of k(f). Factor z(r).
-(r + 1)**3
Factor 0 - 2/9*a**3 - 8/9*a**2 - 2/3*a.
-2*a*(a + 1)*(a + 3)/9
Let r(n) be the third derivative of -n**7/315 + n**6/180 + n**5/30 - n**4/36 - 2*n**3/9 - 9*n**2. Let r(f) = 0. What is f?
-1, 1, 2
Let d(b) be the second derivative of 0*b**4 + 0*b**3 + 1/30*b**6 + 0 - 1/20*b**5 + b + 0*b**2. Factor d(p).
p**3*(p - 1)
Suppose 0 = -24*i + 30*i. Let i*q**2 + 4/5*q**4 + 0 - 6/5*q**3 + 2/5*q = 0. Calculate q.
-1/2, 0, 1
Suppose -889 = -21*l + 245. Let i(w) be the first derivative of 3 - 27*w**2 - l*w - 6*w**3 - 1/2*w**4. What is d in i(d) = 0?
-3
Let n be ((-9)/(-4))/((-3)/12). Let h = n - -11. Solve -5*d**h + d + 4*d**2 + d - d**3 = 0.
-2, 0, 1
Let q = -3 + 21. Let f be (q/21)/((-1)/(-2)). Factor -8/7*j**3 - f*j**2 - 2/7*j**4 - 8/7*j - 2/7.
-2*(j + 1)**4/7
Suppose 0 + 2/7*s**5 + 0*s**3 - 2/7*s - 4/7*s**2 + 4/7*s**4 = 0. What is s?
-1, 0, 1
Let r be 6/21 - (-634)/(-14). Let a be 10/r + 38/9. Let 1/2*d**a + 1/2*d - d**2 + 1/2*d**5 - d**3 + 1/2 = 0. Calculate d.
-1, 1
Suppose 3*j - 4*t - 4 + 3 = 0, -2*t = 4*j - 16. Solve -6 - j*s - 3*s**3 + s + 6*s**2 + 5*s = 0 for s.
-1, 1, 2
Let r(p) = -p**3 - 4*p**2 + 5*p + 2. Let v(c) = c**2 - c - 5. Let d be v(0). Let s be r(d). Factor 0*b**3 - b - 5*b**s + 3*b**2 + 0*b - b**3.
-b*(b + 1)**2
Let v(h) = -h**3 - 4*h**2 + 5*h + 3. Let q be v(-5). Factor -2/3*c**5 + 2/3*c**4 + 0*c**2 + 0 + 0*c**q + 0*c.
-2*c**4*(c - 1)/3
Solve -2/5*m**5 - 2/5*m + 0 + 4/5*m**3 + 0*m**4 + 0*m**2 = 0.
-1, 0, 1
Suppose -2*r - q = -5*q, 5*q = -r. Suppose r = -x - 5*x. Solve x - 2/5*t + 2/5*t**2 = 0.
0, 1
Let u = -227/4 + 57. Suppose 5*x - 12 = -x. Find v such that -1/4*v**4 + v + v**3 - 3/2*v**x - u = 0.
1
Let n be (-2)/(-4)*1*16. Let k be 92/22 + n/(-44). Factor 7*w**4 - 1 + 4*w**3 + 1 + 3*w**k.
2*w**3*(5*w + 2)
Let b(c) = 20*c**3 - 60*c**2 - 20*c + 68. Let u(p) = 7*p**3 - 20*p**2 - 7*p + 23. Let o(h) = 3*b(h) - 8*u(h). Determine g, given that o(g) = 0.
-1, 1, 5
Let k be ((-18)/4)/(6/16). Let p = -7 - k. Factor -n**4 + n - 6*n**3 + 4*n**5 - 1 - n**p + 4*n**3 + 2*n**2 - 2*n**5.
(n - 1)**3*(n + 1)**2
Let b(q) be the third derivative of 0 - 3/5*q**3 - 1/150*q**5 + 0*q - q**2 - 1/10*q**4. Factor b(o).
-2*(o + 3)**2/5
Suppose 7*o = 2*o. Factor -f**2 + 0 + o*f**3 + 1/2*f + f**4 - 1/2*f**5.
-f*(f - 1)**3*(f + 1)/2
Let g(z) = z**2 - z. Let x be g(2). Let j(t) be the first derivative of 1/7*t**2 - 4/7*t + x + 2/21*t**3. Suppose j(r) = 0. Calculate r.
-2, 1
Suppose 3*n = v - 14, -2 = 3*v + 3*n + 4. Suppose -2*p = -o + 4, -v*p + 0*p + 16 = 4*o. Factor z - 3*z**3 + 5*z**