hat -4/3*y**4 - 4/3*y**5 + 0 + 0*y + 32/3*y**3 + 16*y**2 = 0.
-2, 0, 3
Find a such that -1/3*a**3 - 10/3 + 13/3*a - 2/3*a**2 = 0.
-5, 1, 2
Factor -4/3*d + 0 + 1/6*d**2.
d*(d - 8)/6
Let l(x) be the second derivative of x**6/30 + x**5/3 + 7*x**4/6 + 2*x**3 - 9*x**2 + 21*x. Let m(z) be the first derivative of l(z). Factor m(a).
4*(a + 1)**2*(a + 3)
Find o, given that -5/3*o**2 - 16/3 - 16/3*o - 1/6*o**3 = 0.
-4, -2
Let i(y) be the second derivative of y**7/504 + y**6/144 - 35*y**4/12 + 39*y. Let j(x) be the third derivative of i(x). Find n, given that j(n) = 0.
-1, 0
Let d(k) = 3*k + 41. Let l be d(-13). Solve -186*z**5 + l*z**2 + 2*z**3 + 6*z**2 + 188*z**5 - 4*z**3 - 8*z**4 = 0 for z.
-1, 0, 1, 4
Suppose -361 - 15*y**2 + 15*y**3 - 399*y + 10*y**2 - 16*y**3 - 34*y**2 = 0. Calculate y.
-19, -1
Let s be (-41)/(-410)*(11 + 4). Factor 2 + 4*r + s*r**2 - r**3 - 1/2*r**4.
-(r - 2)*(r + 1)**2*(r + 2)/2
Let x = 7/170 - 114/2975. Let j(h) be the third derivative of 1/1680*h**8 + 0 + 1/200*h**6 + 0*h + 0*h**4 - h**2 - 1/300*h**5 - x*h**7 + 0*h**3. Factor j(a).
a**2*(a - 1)**3/5
Let n(q) = q**2 - 2*q + 5. Let x be n(3). Let k be ((x/(-12))/((-1)/(-9)))/(-2). What is g in 0 - 2/3*g**k + 0*g + 1/3*g**2 + 1/3*g**4 = 0?
0, 1
Let f(o) be the third derivative of 7*o**5/15 - 13*o**4/6 + 4*o**3 + o**2 + 44. Factor f(v).
4*(v - 1)*(7*v - 6)
Let m(c) be the second derivative of c**6/72 - c**5/8 + 5*c**4/12 - 13*c**3/6 + c**2 - 51*c. Let q(v) be the second derivative of m(v). What is j in q(j) = 0?
1, 2
Solve 0 + 0*j - 1/2*j**5 + 3*j**2 - 1/2*j**3 - 2*j**4 = 0 for j.
-3, -2, 0, 1
Let y(k) be the first derivative of -k**3 - 24*k**2 + 51*k + 61. Solve y(g) = 0.
-17, 1
Factor 18/19*y**2 + 4/19*y + 22/19*y**4 + 6/19*y**5 + 0 + 30/19*y**3.
2*y*(y + 1)**3*(3*y + 2)/19
Let i be ((-46)/(-8) + (-17 - -11))*0. Let r(s) be the second derivative of 5*s + i*s**3 - 1/160*s**5 + 0*s**2 + 0 - 1/96*s**4. Factor r(u).
-u**2*(u + 1)/8
Let j = -50 + 51. Let o be (2*(j + 2))/((-9)/(-4)). Let -56/3*s - 98/3*s**4 + 30*s**2 + 56/3*s**3 + o = 0. What is s?
-1, 2/7, 1
Let p(v) be the second derivative of v**7/490 - v**6/45 + 4*v**5/105 - 13*v**3/6 - v. Let d(m) be the second derivative of p(m). Solve d(w) = 0.
0, 2/3, 4
Let z be (-51)/17*(-5)/3. Solve 148*r**2 - 7*r - 9*r**z + 25*r**5 + 67*r + 84*r**4 + 8 + 164*r**3 = 0 for r.
-2, -1, -1/4
Let u = 192 - 1724/9. Let g be (-1 + 1)/(-1 + 0). Factor -2/9*s**2 + u*s + g - 2/9*s**3.
-2*s*(s - 1)*(s + 2)/9
Find c such that -59*c**2 + 3*c**3 + 77*c**3 + 6*c**5 + 38*c**4 - 2*c**5 + 9*c**2 = 0.
-5, 0, 1/2
Let c be -4*((-1)/4 - (11198/(-616) - -18)). Determine w so that -c*w**3 + 4*w**2 - 256/7 - 64/7*w = 0.
-2, 8
Suppose 72*g**2 + 3/2*g**4 + 96*g + 0 - 45/2*g**3 = 0. What is g?
-1, 0, 8
Let c(k) be the third derivative of -k**8/84 + 2*k**7/15 - 3*k**6/5 + 4*k**5/3 - 4*k**4/3 - 2*k**2 - 111*k. Solve c(s) = 0 for s.
0, 1, 2
Factor 10 + 61*d**2 - 8*d**3 - 4*d**3 - 9*d**3 - 14 - 36*d.
-(d - 2)*(d - 1)*(21*d + 2)
Let l be 96/36*18*(-6)/8. Let i be (-2 - -5 - 6)*l/189. Solve 6/7*w - i - 2/7*w**2 = 0.
1, 2
Suppose -265 = -2*a + 5*k, a - k - 113 = -5*k. Let p = a + -122. Solve -1/2 - 5/4*b - 7/4*b**4 + 9/4*b**2 + 5/4*b**p = 0 for b.
-1, -2/7, 1
Let h(t) = -7*t**4 + 13*t**3 - 5*t**2 - 13*t + 8. Let y(g) = -13*g**4 + 25*g**3 - 8*g**2 - 25*g + 14. Let s(x) = 7*h(x) - 4*y(x). What is q in s(q) = 0?
-1, 0, 1, 3
Let i(m) be the second derivative of m**4/120 + 47*m**3/60 + 9*m**2/2 + 338*m + 1. Factor i(d).
(d + 2)*(d + 45)/10
Let v be 12/20 + 117/5. Let q be ((-6)/v)/((-1 - -2)/(-8)). Suppose q + 2/9*o**2 - 4/3*o = 0. Calculate o.
3
Let d(o) = 64*o**2 - 8*o - 1. Let q(h) = 22*h**2 - 2*h. Let s(p) = -4*d(p) + 11*q(p). Factor s(r).
-2*(r - 1)*(7*r + 2)
Let p(g) be the first derivative of 0*g**4 + 1/12*g**6 + 0*g + 4 - 1/4*g**2 + 1/3*g**3 - 1/5*g**5. Determine s, given that p(s) = 0.
-1, 0, 1
Let o(u) = 147*u**2 + 18*u - 171. Let x(r) = 41*r**2 + 5*r - 49. Let n(z) = 5*o(z) - 18*x(z). Suppose n(j) = 0. Calculate j.
-3, 3
Let o(v) be the second derivative of 12*v + 1/84*v**4 + 0 + 1/7*v**2 + 1/14*v**3. Determine w, given that o(w) = 0.
-2, -1
Let r(q) be the first derivative of q**3 - 15*q**2 + 27*q + 248. Determine v so that r(v) = 0.
1, 9
Let b = -23 - -23. Suppose b = -6*p + 2*p. Solve p*q**2 - q**2 - 2*q**2 + 2*q**2 + q = 0 for q.
0, 1
Let b be (-8)/44 - (-27)/(-33). Let r = b + 5. Let y(s) = -2*s**2 - 7*s + 7. Let c(g) = g**2 + 7*g - 6. Let x(q) = r*y(q) + 5*c(q). Factor x(k).
-(k - 2)*(3*k - 1)
Let p(i) be the first derivative of 7*i**3/2 + i**2/4 - 28. Suppose p(z) = 0. What is z?
-1/21, 0
Let v(a) = -a**2 - 2*a + 1. Let d(i) = i**3 - 78*i**2 + 1440*i + 2. Let c(r) = 3*d(r) - 6*v(r). Find y such that c(y) = 0.
0, 38
Factor -3/7*k**4 - 1/7*k**2 + 0 + 5/7*k**3 + 0*k - 9/7*k**5.
-k**2*(k + 1)*(3*k - 1)**2/7
Determine h, given that 14 + 11*h - h**2 - 11 + 9*h - 67 = 0.
4, 16
Let j = 120 - 118. Let k be (j - 2)*(-1)/6*-3. Let k + 3/5*s**4 + 0*s**3 - 6/5*s - 9/5*s**2 = 0. What is s?
-1, 0, 2
Let s be (5 - -3) + 400/(-56). Let l(r) be the first derivative of 9/7*r - s*r**2 + 8 + 1/7*r**3. Suppose l(w) = 0. Calculate w.
1, 3
Suppose 0 = 5*j + 4*t + 5, j - 13 = t + t. Find i such that 2*i**4 - i + i**5 + 210*i**2 + 2*i**j - 212*i**2 - 2*i**3 = 0.
-1, 0, 1
What is x in -12/7*x**3 + 0 + 3/7*x**5 + 0*x - 3/7*x**4 + 12/7*x**2 = 0?
-2, 0, 1, 2
Let i(q) be the second derivative of -4*q**4/3 + 78*q**3 - 58*q**2 - 145*q. Suppose i(b) = 0. Calculate b.
1/4, 29
Let g(w) be the third derivative of 1/2*w**3 + 1/30*w**6 - 1/30*w**5 - 1/6*w**4 - 1/210*w**7 + 0 - 6*w**2 + 0*w. Solve g(v) = 0.
-1, 1, 3
Suppose -43 - 32 + 9*f**3 + 75 - 2*f**2 + 11*f**4 = 0. Calculate f.
-1, 0, 2/11
Suppose h - 4*o - 2 = 0, -2*h + 3*h + 2*o = 8. Let a be 4*15/80*4/h. Determine p, given that a*p**5 + 0 - p**4 - 1/2*p + 0*p**3 + p**2 = 0.
-1, 0, 1
Let r(t) = 7*t**2 + 35*t - 38. Let k(v) = 12*v**2 + 71*v - 76. Let s(j) = 4*k(j) - 7*r(j). Determine i, given that s(i) = 0.
1, 38
Factor 3/2*u**5 - 3/2*u**4 + 0 - 3/2*u**3 + 0*u + 3/2*u**2.
3*u**2*(u - 1)**2*(u + 1)/2
Suppose 5*y + 1 = 3*v + 22, -4*y + 20 = -4*v. Determine h so that 2*h**3 + 3*h**y + 3*h**4 - 4*h**3 + 12*h - 10*h**3 = 0.
-1, 0, 2
Factor 6/11*v**3 + 0*v**2 + 2/11*v**4 - 8/11*v + 0.
2*v*(v - 1)*(v + 2)**2/11
Let k(p) be the second derivative of p**6/30 - p**5/5 + p**4/4 + 3*p - 16. Solve k(g) = 0 for g.
0, 1, 3
Let o = 233 - 241. Let g be 2/o*(-8)/6. Let -4/3 + v**2 - g*v**4 - 2/3*v**3 + 4/3*v = 0. Calculate v.
-2, 1
Factor 13/2*s**2 + 8*s - 96 + 1/2*s**3.
(s - 3)*(s + 8)**2/2
Let y(p) be the third derivative of -p**6/420 - 8*p**5/105 + 5*p**4/12 - 6*p**3/7 + 14*p**2 - 3. Solve y(c) = 0 for c.
-18, 1
Let i(y) be the first derivative of 4 - 10/3*y**3 + 0*y**2 - 15/4*y**4 - y**5 + 0*y. Suppose i(g) = 0. What is g?
-2, -1, 0
Let u be ((-1)/(-16))/(62/(-8) - -9). Let n(d) be the third derivative of 0*d + u*d**5 + 0*d**3 - 2*d**2 + 1/8*d**4 + 0. Solve n(x) = 0 for x.
-1, 0
Let j(l) = -6*l**4 + 21*l**3 - 12*l**2 - 3*l + 3. Let m(s) = -11*s**4 + 41*s**3 - 25*s**2 - 5*s + 5. Let v(q) = -5*j(q) + 3*m(q). Find r, given that v(r) = 0.
0, 1, 5
Let s(x) = -3*x**3 + 6*x**2 + 9*x + 12. Let v(a) = 9*a**3 - 18*a**2 - 27*a - 34. Let h(q) = 17*s(q) + 6*v(q). Find u such that h(u) = 0.
-1, 0, 3
Suppose 37*v = 55*v - 36. Solve -4/13*g - 2/13*g**v + 6/13 = 0 for g.
-3, 1
Let m(z) be the second derivative of -z**4/4 - 5*z**3/2 + 54*z**2 - 183*z. Determine n, given that m(n) = 0.
-9, 4
Let -18*u**4 + 12 + 50*u - 38*u**3 - 129*u**2 + 125*u**3 - 2*u = 0. What is u?
-1/6, 1, 2
Let f(j) = 2*j**2 - 46*j + 78. Let y(m) = 5*m**2 - 90*m + 155. Let o(z) = 5*f(z) - 3*y(z). Let o(c) = 0. Calculate c.
3, 5
Let h(j) = 0*j**2 - 5*j**2 + 14*j**2 + 19*j + 41. Let a(v) = -4*v**2 - 10*v - 20. Let p(m) = -5*a(m) - 2*h(m). Solve p(r) = 0.
-3
Let d(p) = 2*p**2 + 232*p - 6732. Let n(q) = 5*q**2 + 696*q - 20195. Let l(m) = 11*d(m) - 4*n(m). Suppose l(j) = 0. Calculate j.
58
Let r(l) = -l**4 - 5*l**3 + 7*l**2 + l + 6. Let k(b) = -5*b**2 + b**3 - b - 1 + 2*b + 4*b**2 + 0*b**3. Let v(z) = 4*k(z) + r(z). Factor v(c).
-(c - 2)*(c + 1)**3
Let x(d) be the first derivative of -8 + 4*d - d**2 - 2/3*d**3. Let x(n) = 0. Calculate n.
-2, 1
Solve 0*a - 4/11*a**4 + 2/11*a**5 + 0 - 14/11*a**3 - 8/11*a**2 =