0, 1
Suppose 20/7*t + 52/7*t**4 + 44/7*t**2 - 8/7*t**5 - 92/7*t**3 - 16/7 = 0. What is t?
-1/2, 1, 4
Determine a, given that 609*a**2 - 599*a**2 - 1 + 7 - 3*a**3 + a**3 - 14*a = 0.
1, 3
Let j(z) be the third derivative of z**6/40 - z**5/4 + z**4 - 2*z**3 + 4*z**2 + 3*z. Let j(f) = 0. Calculate f.
1, 2
Let r = 430 - 185. Let z = r - 2693/11. What is k in 12/11*k**4 - 18/11*k + 32/11*k**2 + 4/11 - 28/11*k**3 - z*k**5 = 0?
1, 2
Suppose 0 = q - 5 - 4. Let z = -4 + q. Determine x so that 2*x**2 - 2*x**4 - 2 - x**2 + x + x**z + 3*x**2 - 2*x**3 = 0.
-1, 1, 2
Let a(n) = n**3 - 3*n**2 - 5*n - 2. Let k be a(5). Let d = 26 - k. Factor -3*q - 3*q**2 + 6*q + d*q**3 - 3*q**2.
3*q*(q - 1)**2
Let b(p) be the first derivative of 4*p - p**4 + 27 - 4/3*p**3 + 2*p**2. Find v, given that b(v) = 0.
-1, 1
Suppose 2*t + 3*c = -2*c - 34, 0 = 3*c + 24. Factor 1/3*i**3 + 0 + t*i + 2*i**2.
i*(i + 3)**2/3
Let g = -315 + 292. Let r(c) = c**2 + 27*c + 92. Let i be r(g). What is n in -1/3*n + i - n**3 - n**2 - 1/3*n**4 = 0?
-1, 0
Let p(h) be the first derivative of -h**3/15 + 9*h**2/2 + 46*h/5 + 314. Factor p(i).
-(i - 46)*(i + 1)/5
Let j = 89/70 - -27/14. Let g = -18561/5 + 3729. What is z in -j + g*z**2 - 106/5*z**3 + 8*z + 28/5*z**4 = 0?
-1/2, 2/7, 2
Let b(g) = -4*g**2 - 30*g - 11. Let o be b(-6). Let v be ((-45)/o)/9 - (-46)/30. Find s such that -2*s**2 - v + 2/3*s**4 - 2/3*s**3 + 10/3*s = 0.
-2, 1
Let x be (-1)/((-352)/28 + 4). Let l(u) be the third derivative of -1/24*u**6 + 0 + 0*u + x*u**5 - u**2 - 1/12*u**4 + 0*u**3. Factor l(s).
-s*(s - 1)*(5*s - 2)
Let z(c) be the first derivative of -c**6/12 - 3*c**5/10 - c**4/8 + c**3/2 + c**2/2 + 220. Determine j so that z(j) = 0.
-2, -1, 0, 1
Let s(k) be the first derivative of -k**3/3 - 10*k**2 - 100*k - 144. Solve s(i) = 0.
-10
Let p(b) = b - 9. Let z be p(11). Let d(k) = 2*k**z - 3*k**2 + 0*k**2. Let l(g) = -g**3 - 2*g**2 - 3*g + 1. Let c(o) = -5*d(o) + l(o). Factor c(h).
-(h - 1)**3
Let o(s) be the second derivative of 0 - 1/12*s**4 - 2/3*s**3 - 4*s - 3/2*s**2. Solve o(p) = 0 for p.
-3, -1
Let y(g) be the third derivative of 3*g**6/40 + 193*g**5/20 - 389*g**4/24 + 65*g**3/6 + 438*g**2. Factor y(u).
(u + 65)*(3*u - 1)**2
Let r(t) be the first derivative of -t**4/6 + 8*t**3/9 + t**2 - 12*t - 72. Solve r(o) = 0 for o.
-2, 3
Suppose 40 + 25 = 5*u. Suppose u*p - 2*f = 10*p, -4*p + 17 = 3*f. Let -3/2*g**2 + g - 5/4*g**3 - 1/4*g**4 + p = 0. Calculate g.
-2, 1
Let h = 477 + -285. Let d = h + -192. Factor -2/7*a**3 + 2/7*a**4 + d + 0*a - 2/7*a**2 + 2/7*a**5.
2*a**2*(a - 1)*(a + 1)**2/7
Let o = -105 - -108. Factor -3243*n - 4*n**o + 3243*n.
-4*n**3
Let y = 272 + -2440/9. Let b(r) be the first derivative of 2 - 1/18*r**4 + y*r - 2/9*r**3 + 0*r**2. Factor b(h).
-2*(h - 1)*(h + 2)**2/9
Let x = 2959 + -11831/4. Let b(h) be the first derivative of -25/4*h + 1 - x*h**2 - 1/12*h**3. Let b(t) = 0. What is t?
-5
Let o = 7/4 + -437/252. Let a(u) be the second derivative of 1/3*u**3 - 5*u - 1/15*u**5 + 0 - o*u**7 - 1/3*u**2 - 1/9*u**4 + 1/15*u**6. Factor a(l).
-2*(l - 1)**4*(l + 1)/3
Let y(g) = 5*g**5 - 6*g**4 - 9*g**3 + 2*g**2 + 4*g - 4. Let s(n) = -n**5 + n**4 + n + 1. Let t(p) = -4*s(p) - y(p). Find u, given that t(u) = 0.
-2, -1, 0, 1, 4
Let c = 5/543 + 523/2172. Solve 0*q**4 + 0 + c*q**5 + 1/4*q + 0*q**2 - 1/2*q**3 = 0 for q.
-1, 0, 1
Let q(s) = -4*s**2 + 2*s + 9. Let i(b) = -23*b**2 + 11*b + 51. Let y(n) = -6*i(n) + 34*q(n). Factor y(k).
2*k*(k + 1)
Let o(b) be the first derivative of -6/5*b**2 - 1/5*b**3 + 7 - 12/5*b. Factor o(i).
-3*(i + 2)**2/5
Let i(p) = 265*p + 20935. Let a be i(-79). Suppose 3*k**3 + a*k + 3/2*k**4 + 0 + 3/2*k**2 = 0. Calculate k.
-1, 0
Let q(h) be the second derivative of 0 + 1/60*h**4 + 1/15*h**3 + 1/10*h**2 - 16*h. Solve q(u) = 0 for u.
-1
Let v(n) be the second derivative of n**6/6 - 19*n**5/20 + n**4/12 + 31*n**3/6 + 3*n**2 - 49*n. Suppose v(o) = 0. Calculate o.
-1, -1/5, 2, 3
Let h(m) = -m**3 - 4*m**2 + 2. Let a be h(-4). Let p(u) = u**3 - 5*u**2 + 4. Let t be p(5). Solve b + 4*b**a - b - 7*b**2 + 3*b**t = 0 for b.
-1, 0, 1
Let x(r) be the second derivative of 1/168*r**7 + 0*r**3 + 0*r**4 + 4*r - 1/40*r**6 + 0 + 0*r**2 + 1/40*r**5. Suppose x(p) = 0. Calculate p.
0, 1, 2
Suppose 2*l = 4*c - 10, -2*l + 5*l - 5*c + 12 = 0. Find d such that -25*d + 19 + 4*d**2 + 5*d**2 - 4*d**2 + l = 0.
1, 4
Solve 4*s**2 - 2*s**5 - 4*s**4 + 26 - 33 + 2*s + 7 = 0.
-1, 0, 1
Factor 0*p + 21/5*p**4 + 24/5*p**2 + 18*p**3 + 0.
3*p**2*(p + 4)*(7*p + 2)/5
Let z(u) = u**3 + 9*u**2 - u + 9. Let t be z(-8). Suppose 0 = -9*f + 6*f + t. Factor -24*r**2 - 30*r**4 + 6*r**5 + 108*r**3 - 3*r**5 - f*r**2 - 111*r**2 + 81*r.
3*r*(r - 3)**3*(r - 1)
Let i(m) = -m**3 + 4*m**2 - 8. Let s be i(-9). Determine a, given that 1045*a - s*a - 3*a**2 = 0.
0
Let n(y) be the second derivative of -y**2 + 0 + 1/36*y**4 + 1/18*y**3 - 20*y. Factor n(c).
(c - 2)*(c + 3)/3
Find c, given that -111/5*c**2 + 108/5*c**3 + 0 + 3/5*c = 0.
0, 1/36, 1
Let k = 11163/22334 + 2/11167. Factor k*s**4 + 0*s**3 - 4*s - 3*s**2 - 3/2.
(s - 3)*(s + 1)**3/2
Let m(z) be the second derivative of z**4/3 - 8*z**3 + 72*z**2 + 297*z. Determine c so that m(c) = 0.
6
Suppose 48/5 + 36/5*h - 48/5*h**2 + 0*h**4 - 39/5*h**3 + 3/5*h**5 = 0. Calculate h.
-2, -1, 1, 4
Let i = -41 - -44. Factor -4 + 2 + 25*f**i - 132*f**2 - f**3 + 124*f**2 - 14*f.
2*(f - 1)*(2*f + 1)*(6*f + 1)
Let j(m) be the second derivative of -3/25*m**5 + 3*m + 13/30*m**4 + 4/5*m**2 + 0 - 4/5*m**3 + 1/75*m**6. Factor j(u).
2*(u - 2)**2*(u - 1)**2/5
Suppose -22 + 31 = 89*a - 169. Solve -21/8*i**3 - 3/8 - 27/8*i**a - 15/8*i - 3/4*i**4 = 0 for i.
-1, -1/2
Let r(a) = -52*a**2 + 40*a + 248. Let v(x) = -18*x**2 + 13*x + 83. Let z(n) = 3*r(n) - 8*v(n). Determine l, given that z(l) = 0.
-2, 10/3
Suppose -1225 - 1/4*c**2 - 35*c = 0. What is c?
-70
Let i(p) be the first derivative of -p**4/8 + p**3/6 + p**2/4 - p/2 + 8. Find c, given that i(c) = 0.
-1, 1
Let s be 18/510*-515 - -19. Factor -s*i - 6/17 - 10/17*i**2 - 2/17*i**3.
-2*(i + 1)**2*(i + 3)/17
Let t(x) be the third derivative of 5*x**4/24 + 19*x**3/2 + 9*x**2 - 3. Let g be t(-11). Let 0*h - 6/5*h**4 + 2/5*h**5 + 0 + 0*h**g + 4/5*h**3 = 0. Calculate h.
0, 1, 2
Suppose 165/2 + 3/4*d - 3/4*d**3 - 165/2*d**2 = 0. Calculate d.
-110, -1, 1
Let r(m) be the first derivative of 5/6*m**4 + 1/15*m**5 + 10 + 37/9*m**3 + 10*m**2 + 12*m. Factor r(n).
(n + 2)**2*(n + 3)**2/3
Let a(u) be the third derivative of -21/16*u**4 - 1/20*u**6 - 5/4*u**3 + 0*u + 13*u**2 - 3/5*u**5 + 0. What is w in a(w) = 0?
-5, -1/2
Let j(l) be the third derivative of -l**5/300 + 11*l**4/60 + 616*l**2. Determine p, given that j(p) = 0.
0, 22
Let p = 778 + -778. Suppose -b + 10 = -0*b - 5*c, -4*b = 4*c + 8. Find z such that 0*z**2 + b*z - 2/5*z**3 + p = 0.
0
Let o(i) be the first derivative of 5/4*i**4 + 0*i**3 + 0*i + 0*i**2 - 9. Factor o(h).
5*h**3
Let n = 90344/35 - 18066/7. Factor -2/5*g**4 + 2/5*g**5 + n*g**2 - 2/5*g**3 + 0 + 0*g.
2*g**2*(g - 1)**2*(g + 1)/5
Let t(x) be the second derivative of x**6/60 - 87*x**5/40 - x**4/24 + 29*x**3/4 - 621*x. Determine i so that t(i) = 0.
-1, 0, 1, 87
Let d be 48/336 - 1/((-28)/206). Let 15*k**3 + d*k + 15*k**2 + 3/2*k**5 + 15/2*k**4 + 3/2 = 0. Calculate k.
-1
Let v = -11 - -6. Let s(l) = -l**2 - l. Let m(j) = -10*j**2 - 12*j - 2. Let z(n) = v*m(n) + 35*s(n). Factor z(a).
5*(a + 1)*(3*a + 2)
Factor -167/4*o**2 + 1/4*o**4 + 1936 + 132*o - 3/2*o**3.
(o - 11)**2*(o + 8)**2/4
Let f = 75822 + -681724/9. Let h = 75 - f. Let 0 + 1/9*d**3 + h*d**2 + 0*d = 0. Calculate d.
-1, 0
Let b = -24 - -25. Factor -2 + 12*t - b - 18*t**2 - 2*t**3 - 3*t**4 + 14*t**3.
-3*(t - 1)**4
Let j(n) = 83*n + 583. Let c be j(-7). What is l in 14/17*l**c + 6/17*l**3 - 8/17 + 0*l = 0?
-2, -1, 2/3
Determine v so that -1/7*v**2 - 18/7*v - 81/7 = 0.
-9
Factor 3/2*a**2 + 57/2*a + 27.
3*(a + 1)*(a + 18)/2
Let n = 1223/1606 - 5/146. Let l(t) be the first derivative of -n*t**3 - 9/11*t**2 - 5/22*t**4 - 7 - 4/11*t. Solve l(f) = 0.
-1, -2/5
Let t be 4 - (5 + -1) - -3. Find y such that -92*y**4 - y - 58*y**2 - 12*y**4 - 3*y + 8 + 136*y**t + 28*y**5 - 6*y**2 = 0.
-2/7, 1
Let j(i) be the first derivative of i**4/8 - 8*i**3/3 + 7*i**2 - 706. Factor j(x).
x*(x - 14)*(x - 2)/2
Let t = 512 - 2557/5. Factor 9/5*o - t*o**2 - 6/5.
