117/2*g**2 + 7803 - 107/2*g**3 - 13617/2*g = 0 for g.
2, 3, 51
Let f(i) be the second derivative of -2/15*i**6 - 3*i - 2 + 2/21*i**7 - 4/3*i**3 + 0*i**2 - 3/5*i**5 + 5/3*i**4. Find q such that f(q) = 0.
-2, 0, 1
Let a(u) = u**2 - 82*u + 3. Let d be a(0). Suppose 4*z + d*q = 57, 7*z - 4*q - 45 = 27. Let -2/3*n**2 + z*n - 54 = 0. What is n?
9
Let u(d) be the third derivative of 0*d**3 + d - 1/2*d**4 + 1/840*d**7 + 97/240*d**5 + 0 - 5/48*d**6 - 18*d**2. Suppose u(y) = 0. What is y?
0, 1, 48
Let j(g) be the first derivative of -g**5/10 + 13*g**4/2 - 475*g**3/6 + 237*g**2 + 738*g - 2988. Factor j(u).
-(u - 41)*(u - 6)**2*(u + 1)/2
Suppose -3*s - 4*q = -4, -51*q - 10 = -5*s - 56*q. Find r, given that 4/9*r + 2/9*r**s - 4/9*r**3 - 2/9 + 0*r**2 = 0.
-1, 1
Let s(r) = -38*r**2 + 11856*r. Let b(l) = 29*l**2 - 8892*l. Let q(a) = -13*b(a) - 10*s(a). Suppose q(n) = 0. Calculate n.
0, 988
Let s(i) be the third derivative of 0*i**3 - 2*i**2 + 10/9*i**4 + 5/18*i**5 - 1/42*i**7 - 55*i - 23/72*i**6 + 0. Find t such that s(t) = 0.
-8, -2/3, 0, 1
Let q(j) be the second derivative of 0*j**2 + 2 + 1/75*j**6 + 23*j + 1/6*j**4 + 2/15*j**3 + 2/25*j**5. Suppose q(g) = 0. Calculate g.
-2, -1, 0
Let d(f) = -6*f**2 - 8*f + 5. Let t be d(9). Let x = 553 + t. Determine z, given that -4/3*z**3 - 2/3*z**4 + 2/3*z**2 + x + 4/3*z = 0.
-2, -1, 0, 1
Let p = 769/4890 + -28/489. Let y(u) be the first derivative of 14/15*u**3 - p*u**4 + 17/5*u**2 + 18/5*u - 36. Factor y(v).
-2*(v - 9)*(v + 1)**2/5
Let z(q) be the second derivative of -q**4/6 + 5*q**3 - 14*q**2 + 124*q + 1. Suppose z(p) = 0. Calculate p.
1, 14
Let a = 21630/11 + -108106/55. Factor -a*h - 2/5*h**2 + 4/5*h**3 + 0 + 2/5*h**4.
2*h*(h - 1)*(h + 1)*(h + 2)/5
Let v(y) be the third derivative of -5*y**6/24 - 19*y**5/6 - 55*y**4/6 + 20*y**3 - 2086*y**2 - y. Suppose v(t) = 0. What is t?
-6, -2, 2/5
Let r(h) be the first derivative of -6/35*h**5 + 62 + 0*h - 33/28*h**4 + 12/7*h**3 + 54/7*h**2 + 1/14*h**6. What is t in r(t) = 0?
-2, 0, 3
Let y(g) be the second derivative of g**7/4200 - g**6/1200 - g**5/100 + 7*g**4/4 + 44*g. Let q(c) be the third derivative of y(c). Factor q(k).
3*(k - 2)*(k + 1)/5
Suppose 52 - 38 = 7*b. What is i in -i**5 + 17154*i**3 + 2*i**4 - 17154*i**3 + i - b*i**2 = 0?
-1, 0, 1
Let n be -1*7 - 8/(-6)*9. Let z(f) be the second derivative of -3*f + 0*f**2 - 1/15*f**n - 2/3*f**4 - 2*f**3 + 0. Determine c so that z(c) = 0.
-3, 0
Let o be 18*((-16)/24)/(-2). Suppose -3*c = -3*u - o, 4 = -5*u + 3*c - c. Factor -2/3*l + u + 2/9*l**2.
2*l*(l - 3)/9
Suppose -13*u = 48 - 113. Let t(j) = 2*j**3 - 23*j**2 - 22*j - 7. Let n(p) = -p**3 + p**2 - p - 1. Let q(b) = u*n(b) + t(b). Suppose q(r) = 0. Calculate r.
-4, -1
Suppose -252/5 - 3/5*f**3 + 111/5*f + 0*f**2 = 0. What is f?
-7, 3, 4
Let r = 130839 + -1439211/11. Suppose -145/11*k - 75/11 - 1/11*k**5 + r*k**3 - 58/11*k**2 + 5/11*k**4 = 0. What is k?
-3, -1, 5
Let c = 545 - 541. Let y(q) = 2*q**4 + q**3 - q**2 + q. Let j(x) = 2*x**4 - 4*x**3 + 6*x**2 + 2*x. Let p(a) = c*y(a) - 2*j(a). Solve p(i) = 0.
-4, 0, 1
Let p(a) be the second derivative of 1/24*a**4 + 0 + 13/3*a**3 + 169*a**2 + 7*a. Solve p(f) = 0 for f.
-26
Let k(y) be the second derivative of -13/399*y**7 + 2/57*y**3 - 37/285*y**6 - 33/190*y**5 - y - 7/114*y**4 + 0*y**2 + 35. Determine m so that k(m) = 0.
-1, 0, 2/13
Let l(t) be the second derivative of t**4/18 - 19*t**3/3 - 58*t**2/3 - 165*t - 5. Solve l(i) = 0 for i.
-1, 58
Let r = 1777 - 1777. Let x(j) be the third derivative of 0 - 1/12*j**3 - 21*j**2 + r*j + 1/240*j**5 + 1/96*j**4. Factor x(y).
(y - 1)*(y + 2)/4
Let v(h) be the first derivative of h**4/8 + 23*h**3/3 + 155*h**2 + 1300*h + 264. Factor v(u).
(u + 10)**2*(u + 26)/2
Let 9*v**4 - 1976 + 1964*v**3 + 24739*v - 5916*v**2 - 18815*v - 5*v**4 = 0. Calculate v.
-494, 1
Let i(n) = n**3 - 4*n**2 + 4*n - 14. Let f be i(4). Suppose 143*u**4 - 8*u + 2*u**2 - 4*u**5 + 2*u**f + 12*u**3 - 147*u**4 = 0. What is u?
-2, -1, 0, 1
Let c = 2/88285 + 176548/971135. Suppose 86/11*p - c*p**3 - 4 - 40/11*p**2 = 0. Calculate p.
-22, 1
Determine k so that -2*k - 25144*k**3 - 6*k**4 + 25150*k**3 + 12*k**2 - k - 3*k**5 - 6 = 0.
-2, -1, 1
Let h = -7610 - -7616. Factor -1/2*r**4 - 3*r**3 - 9/2*r**2 + h + 2*r.
-(r - 1)*(r + 2)**2*(r + 3)/2
Let q(b) = -9*b - 536. Let o be q(-54). Let y be -6 + ((-310)/o - (-2)/5). Find x such that -1/5*x**2 + 4/5 - y*x = 0.
-4, 1
Let p(w) be the second derivative of 1/10*w**6 - w**4 - 3/2*w**5 + 3*w + 0*w**2 + 12*w**3 + 1/14*w**7 + 10. Factor p(f).
3*f*(f - 2)**2*(f + 2)*(f + 3)
Let j(r) be the third derivative of r**5/30 - 593*r**4/12 + 592*r**3/3 + 815*r**2. Factor j(b).
2*(b - 592)*(b - 1)
Let f = 104158 - 312466/3. Factor 0 + 4/3*y**3 + 4/3*y - f*y**2.
4*y*(y - 1)**2/3
Let s(a) be the second derivative of 38*a**3 - 14/3*a**4 - 27*a + 1/5*a**5 - 144*a**2 - 3. Let s(j) = 0. Calculate j.
3, 8
Factor 3/4*p**3 - 1050 + 9/2*p**2 - 135*p.
3*(p - 14)*(p + 10)**2/4
Let k = -6607 + 6625. Let h(g) be the first derivative of k*g**2 + 4/3*g**3 + 0*g + 42. Factor h(j).
4*j*(j + 9)
Factor -b**2 - 156302 - 54331 + 838*b + 35072.
-(b - 419)**2
Let u(g) = 2*g**2 + g + 1. Suppose -5*p = 4*l + 33, 2*p = -6 - 4. Let y(m) = -m**2 - 3. Let c(j) = l*u(j) - 2*y(j). Factor c(v).
-2*(v - 1)*(v + 2)
Let u(m) be the third derivative of m**6/280 + 177*m**5/140 + 25*m**4/4 - 1912*m**2 - 3. Factor u(q).
3*q*(q + 2)*(q + 175)/7
Let o be ((-1)/((-2)/(-3)))/(5/(-10)). Suppose 18*f = 19*f - o. What is q in 4*q**2 + 0 + 0*q + 4/3*q**f = 0?
-3, 0
Let k(s) be the first derivative of s**3/12 - 753*s**2/4 - 1507*s/4 + 13549. Suppose k(m) = 0. What is m?
-1, 1507
Let a(r) = 9*r**3 - r + 3*r**3 - 6*r**3 - 5*r**3 - 1. Let f(d) = -5*d**4 - 41*d**3 - 40*d**2 + 86*d + 6. Let x(c) = 6*a(c) + f(c). Find u, given that x(u) = 0.
-4, 0, 1
Let n = 6354 + -95309/15. Let b(q) be the second derivative of -1/6*q**4 + 0*q**2 + 0 - 1/21*q**7 + 13*q + 1/10*q**5 + 0*q**3 + n*q**6. Factor b(h).
-2*h**2*(h - 1)**2*(h + 1)
What is j in 25 + 4 - 142 + 41 - 2*j**3 + 82*j - 8*j**2 = 0?
-9, 1, 4
Let i(b) = 70*b - 200. Let d be i(3). Let w be (12 - (3 + 15))*d/(-78). Find y, given that -2/13*y**4 - w*y**3 + 0 + 0*y - 8/13*y**2 = 0.
-4, -1, 0
Factor 3/5*z**3 - 1323/5*z + 663/5 + 657/5*z**2.
3*(z - 1)**2*(z + 221)/5
Let z(k) be the first derivative of 4*k**5 + 5/4*k**4 - 40*k + 5/6*k**6 - 50*k**2 - 70/3*k**3 + 126. Find h such that z(h) = 0.
-2, -1, 2
Let a = -44586/5 + 133778/15. Determine j, given that 1/3*j**4 - a - 8/3*j - 1/3*j**2 + 5/3*j**3 - 1/3*j**5 = 0.
-1, 2
Let t(i) = 8*i**3 - 19*i**2 + 10*i + 12. Let m(r) = -41*r**3 + 94*r**2 - 49*r - 60. Let u be 7*(0 + 0 + (-6)/(-21)). Let g(a) = u*m(a) + 11*t(a). Factor g(o).
3*(o - 2)**2*(2*o + 1)
Let s(m) be the second derivative of 4*m**6/135 - m**5/6 - 16*m**4/3 - 335*m**3/27 - 22*m**2/3 - 2*m + 264. Find d, given that s(d) = 0.
-6, -1, -1/4, 11
Let -1/3*c**4 + 0 - 8/3*c**3 + 37/3*c**2 + 44/3*c = 0. What is c?
-11, -1, 0, 4
Let r(k) = 7*k - 173. Let z be r(25). Factor -99*f + 29*f - 35*f**z - 5*f**3 - 5667 + 5627.
-5*(f + 1)*(f + 2)*(f + 4)
Let x = -3985 + 19929/5. Let t(b) be the first derivative of 16 - 26/45*b**3 + x*b**2 - 2/75*b**5 - 8/15*b + 1/5*b**4. Solve t(q) = 0 for q.
1, 2
Let l(z) be the first derivative of -z**6/27 + 4*z**5/15 - z**4/18 - 16*z**3/9 + 20*z**2/9 - 4999. Suppose l(m) = 0. What is m?
-2, 0, 1, 2, 5
Factor 5*d**3 - 180*d**2 - 2*d**3 - 1739 + 54*d**2 + 243*d + 1619.
3*(d - 40)*(d - 1)**2
Suppose -758 + 1363 = 11*h. Suppose 0*u = -5*o - 2*u + 15, o + 15 = -4*u. Factor -8*r**5 + 23*r**o - 80*r**4 + r**5 - 10*r**2 + h*r**3 + 19*r**5.
5*r**2*(r - 1)**2*(7*r - 2)
Let d(w) be the third derivative of w**8/2016 - w**7/126 + w**6/60 + 17*w**5/180 - 13*w**4/144 - 2*w**3/3 - 676*w**2 - 1. Solve d(x) = 0 for x.
-1, 1, 3, 8
Suppose 0 = 5*o - 4*o. Let p be o/((-2)/(1 - (1 + 2))). Find c such that 5*c**5 - c - 5*c**3 + p*c**5 + c = 0.
-1, 0, 1
Let z(a) be the second derivative of -a**5/10 - 2*a**4/3 + 5*a**3/3 - 103*a. Factor z(g).
-2*g*(g - 1)*(g + 5)
Let z(c) be the third derivative of c + 1/448*c**8 - 1/12*c**3 - 1/60*c**6 - 11/96*c**4 - 3/40*c**5 + 14*c**2 + 1/210*c**7 + 0. Solve z(m) = 0.
-1, -1/3, 2
Let y(a) be the first derivative of -2*a**3/3 - 4*a**2 + 792*a - 4866. Determine n, given that