2
Let h = -5979/5 + 5983/5. Suppose 4/5*c - 2/5*c**2 - h*c**3 + 0 + 2/5*c**4 = 0. What is c?
-1, 0, 1, 2
Factor 870 + 126*t + 2*t**2 - 45 + 3*t**3 + t**2 - 6*t**3 + 129*t.
-3*(t - 11)*(t + 5)**2
Let z(x) be the third derivative of 0 - 16/3*x**4 - 1/420*x**7 - 1/15*x**6 + 5*x**2 - 64/3*x**3 - 4/5*x**5 + 0*x. Factor z(s).
-(s + 4)**4/2
Let q = 119/52 - 20/13. Let u(j) be the first derivative of q*j**2 - 6 + j + 1/6*j**3. Factor u(m).
(m + 1)*(m + 2)/2
Let p(o) be the second derivative of -o**6/60 + 3*o**5/40 - o**4/8 + o**3/12 + o + 8. Factor p(g).
-g*(g - 1)**3/2
Let w be (24/(-10))/((-24)/80). Suppose 2*c = -2*c + w. Factor 2*m**5 - 6*m**3 + m + c*m**3 + 0*m + m.
2*m*(m - 1)**2*(m + 1)**2
Suppose 12 = 7*f - 4*f. Factor 3*d - 2*d**3 - 2*d**2 + 216 - d**5 - 217 + 3*d**4 + 0*d**f.
-(d - 1)**4*(d + 1)
Let z(c) be the first derivative of c**5/15 + 17*c**4/36 + 8*c**3/9 + c**2/2 + 29*c - 9. Let o(s) be the first derivative of z(s). What is v in o(v) = 0?
-3, -1, -1/4
Let n = -7/6 - 4/3. Let g = n + 3. Factor -3/2 - g*y**2 - 2*y.
-(y + 1)*(y + 3)/2
Let q be 1*8 + (-17746)/2335. Determine m so that -12/5*m - q*m**2 + 14/5 = 0.
-7, 1
Let u(j) be the first derivative of -j**4/16 + j**3/6 - j**2/8 + 34. Factor u(h).
-h*(h - 1)**2/4
Let q(n) be the first derivative of -2/33*n**3 + 1/11*n**2 + 5 - 1/22*n**4 + 2/55*n**5 + 0*n. Factor q(l).
2*l*(l - 1)**2*(l + 1)/11
Find t, given that 1/4*t**3 + 3/2 + 1/4*t - t**2 = 0.
-1, 2, 3
Let i(g) be the first derivative of g**6/4 + 3*g**5/10 - 21*g**4/8 - 13*g**3/2 - 9*g**2/2 + 112. Solve i(c) = 0.
-2, -1, 0, 3
Let x be -6 - -16 - 297/30. Let r(b) be the first derivative of 0*b + 3 + 1/15*b**3 + x*b**2. What is n in r(n) = 0?
-1, 0
Let z be (2/(-2))/(4/(-8)). Suppose -5*y - 5*x = -15, -3 = -z*y + x - 4*x. Determine k so that 6*k**2 - y*k + 5*k - 5*k**2 = 0.
0, 1
Let z = 5128/5 + -1025. Factor -1/10*u**4 - 2/5*u**3 - 2/5*u - z*u**2 - 1/10.
-(u + 1)**4/10
Let i(f) = 5*f**4 + 125*f**3 - 125*f**2 + 30*f. Let l(m) = -21*m**3 + 2*m - m**4 - m - 308*m**2 - 6*m + 329*m**2. Let g(t) = -6*i(t) - 35*l(t). Solve g(y) = 0.
0, 1
What is g in 107/9*g + 103/9 + 4/9*g**2 = 0?
-103/4, -1
Let a(f) be the first derivative of -3/11*f**2 - 32 + 0*f + 2/33*f**3. Factor a(w).
2*w*(w - 3)/11
Let r = -187807/70 + 2683. Let o(u) be the second derivative of r*u**5 + 0 + 0*u**4 - 1/105*u**6 - 4/21*u**3 + 0*u**2 + u. Solve o(i) = 0.
-1, 0, 2
Let i = -1345 - -6747/5. Determine c so that -6/5*c**4 - 24/5*c**2 + i*c**3 + 0 + 8/5*c = 0.
0, 2/3, 1, 2
Let z(l) be the second derivative of 5*l**4/32 - 43*l**3/16 - 27*l**2/8 - 84*l. Factor z(p).
3*(p - 9)*(5*p + 2)/8
Let u(g) be the second derivative of -3*g**6/35 - 12*g**5/7 - 31*g**4/42 + 36*g**3/7 + 52*g**2/7 + 257*g. Find j such that u(j) = 0.
-13, -2/3, 1
Let q(k) be the third derivative of -3*k**6/40 + 17*k**5/20 - 9*k**4/4 - 4*k**3 - 448*k**2. Determine y so that q(y) = 0.
-1/3, 2, 4
Let k = -212 + 217. Suppose -23 = -a - 2*t, -t = 2*a - 46 - 0. Determine o so that 20*o**2 - 7*o**3 - 15*o**4 + 5*o**5 - 29*o**3 - 5*o**4 + 8*o + a*o**k = 0.
-1, -2/7, 0, 1
Let o(w) be the third derivative of 4/135*w**5 - 4/945*w**7 + 0*w - 1/90*w**6 + 0 + 2/27*w**4 + 0*w**3 + 1/756*w**8 + 15*w**2. What is d in o(d) = 0?
-1, 0, 2
Let q(a) = 3*a**3 + 6*a**2 - a. Let l(r) = -r**2 - 447*r**3 - 4*r**2 + 445*r**3. Let w(d) = 4*l(d) + 3*q(d). Suppose w(c) = 0. What is c?
-1, 0, 3
Let k(y) be the third derivative of -5*y**8/168 - 16*y**7/105 - 7*y**6/30 + 2*y**5/15 + 11*y**4/12 + 4*y**3/3 - 127*y**2. Factor k(h).
-2*(h + 1)**4*(5*h - 4)
Suppose 0 = -0*d - 4*d - 52. Let s = d + 15. Factor 4*i**3 + 6*i**2 + 0*i - 5*i + 4*i**4 + i - 10*i**s.
4*i*(i - 1)*(i + 1)**2
Let m(v) = -4*v + 6. Let q be m(-9). Let w be q/12 - (-3)/(-6). Let -2*o + 3*o**2 + 0*o + 8*o - 3*o**w = 0. Calculate o.
-1, 0, 2
Let l(n) be the first derivative of 0*n - 3/28*n**4 + 0*n**2 + 9/35*n**5 - 25 + 1/14*n**6 - 3/7*n**3. Suppose l(x) = 0. What is x?
-3, -1, 0, 1
Let s(z) be the third derivative of -z**8/4032 + z**7/504 - 7*z**5/60 - 12*z**2. Let h(l) be the third derivative of s(l). Determine f so that h(f) = 0.
0, 2
Let l(u) = -u**2 - 3*u + 2. Let h(a) = 16*a**2 + 4*a - 200. Let k(s) = -h(s) - 20*l(s). Suppose k(j) = 0. Calculate j.
-10, -4
Let a = 8535 - 42672/5. Suppose a*c**2 + 0 + 0*c = 0. What is c?
0
Let j(g) be the first derivative of g**6/1260 - g**5/90 - 21*g**2 + 39. Let h(m) be the second derivative of j(m). Find n such that h(n) = 0.
0, 7
Let p(w) be the third derivative of -w**6/60 + 17*w**5/10 + 35*w**4/4 + 53*w**3/3 - 9*w**2 - 5. Factor p(t).
-2*(t - 53)*(t + 1)**2
Let q = 1584/7 + -226. Let v = 1/21 + q. Factor 0 - 1/3*k**5 + 0*k - v*k**3 + 2/3*k**4 + 0*k**2.
-k**3*(k - 1)**2/3
Let v(a) be the second derivative of 0 - 1/66*a**3 + 20*a - 1/11*a**2 + 1/132*a**4. Solve v(r) = 0.
-1, 2
Let k(c) = 5*c**2 + 14*c - 17. Let i be k(1). Solve 0 + 3*t**i + 12/5*t**3 + 3/5*t**4 + 6/5*t = 0 for t.
-2, -1, 0
Let f(c) = 2*c + 24. Let p be f(-10). Factor 13*x**2 - 25*x**2 + 9*x**2 + 10*x**p - 14*x**3 + 9*x**2 - 2*x**5.
-2*x**2*(x - 3)*(x - 1)**2
Let u(l) = -l**4 - 47*l**3 - 96*l**2 + 141*l. Let w(p) = -p + p**4 + 3 - 17 - p**3 + 14. Let i(j) = -u(j) + 3*w(j). Factor i(a).
4*a*(a - 1)*(a + 6)**2
Factor -19*k**3 + 81*k**3 - 49 + 29*k**2 + 331*k**5 - 63*k - 330*k**5 + 5*k**2 + 15*k**4.
(k - 1)*(k + 1)**2*(k + 7)**2
Let l(g) be the third derivative of 0 + 25/12*g**4 + 0*g**3 + 1/12*g**5 + 0*g + 10*g**2. Factor l(i).
5*i*(i + 10)
Let y = -16 - -20. Find v such that -2*v**2 - 17*v**y - 22*v**2 + 104*v**3 - 12*v + 4 - 91*v**4 + 36*v**5 = 0.
-1/3, 1/3, 1
Let y = 17/103 - -18/515. Suppose y*o**2 + 1/5*o + 0 = 0. What is o?
-1, 0
Suppose -7 = j - 5*z, 6 = 4*j + 2*z - 5*z. Factor 39*k**4 + k**j - 23*k**4 - 17*k**4 - k + k**2.
-k*(k - 1)**2*(k + 1)
Let s(a) = -2*a**4 - 34*a**3 + 21*a**2 + 113*a - 83. Let k(z) = -25*z**4 - 440*z**3 + 275*z**2 + 1470*z - 1080. Let t(m) = -3*k(m) + 40*s(m). Factor t(f).
-5*(f - 1)**2*(f + 2)*(f + 8)
Let i(j) be the third derivative of -j**8/672 + j**7/105 + j**6/240 - j**5/30 - 18*j**2. Let i(u) = 0. What is u?
-1, 0, 1, 4
Let u = 3/97 - -25/2328. Let m(p) be the third derivative of 0 + 0*p**3 - 1/105*p**7 - 1/336*p**8 + 0*p**6 + 1/30*p**5 + u*p**4 + 9*p**2 + 0*p. Factor m(z).
-z*(z - 1)*(z + 1)**3
Let q + 72 - 4*q**3 + 0*q**3 + 23*q**2 + 3*q - 91*q**2 - 4*q**2 = 0. Calculate q.
-18, -1, 1
Let c be (-158)/(-632) - (1/10 - 0). Let d(u) be the third derivative of -19/40*u**5 + 4*u**2 + 0 - 7/12*u**4 + 0*u - c*u**6 - 1/3*u**3. Factor d(j).
-(3*j + 2)**2*(4*j + 1)/2
Let i(k) = -k**2 + 8*k + 9. Let s be i(9). Suppose 118*x - 5*x = 339. Factor s + 0*b + 2/3*b**2 + b**x + 1/3*b**4.
b**2*(b + 1)*(b + 2)/3
Suppose -10*p + 5*p = 5. Let k be 4/8*(11 - p). Let j(i) = 7*i**2 - 4*i. Let q(o) = 8*o**2 - 5*o. Let g(z) = k*q(z) - 7*j(z). Determine x so that g(x) = 0.
-2, 0
Determine t, given that -78 - 152/3*t**2 - 4*t**3 - 124*t + 2/3*t**4 = 0.
-3, -1, 13
Let x(g) be the first derivative of -g**3/9 - 11*g**2 - 248. Factor x(t).
-t*(t + 66)/3
Let d = -10 + 13. Factor 8*j**2 + 5*j - d*j - 6*j**2 + 14*j + 32.
2*(j + 4)**2
Let q(c) be the second derivative of -2*c**6/15 - 2*c**5/5 + 4*c**4 + 16*c**3/3 - 64*c**2 - 117*c. Factor q(z).
-4*(z - 2)**2*(z + 2)*(z + 4)
Let b(k) be the third derivative of -k**5/60 + k**4/4 + 7*k**3/6 + 181*k**2. Suppose b(z) = 0. Calculate z.
-1, 7
Let l(r) be the first derivative of r**3/18 + 11*r**2/12 + 5*r/3 - 19. Solve l(q) = 0 for q.
-10, -1
Let z be 108/6*12/36. Let v(q) be the third derivative of 0*q**4 - 7*q**2 + 1/90*q**5 - 1/180*q**z + 0*q**3 + 0 + 0*q. Find p such that v(p) = 0.
0, 1
Let j(q) be the third derivative of 0*q - 1/35*q**7 - 52*q**2 - 1/180*q**6 + 1/5*q**5 + 0 + 2/9*q**4 + 0*q**3 + 1/252*q**8. Solve j(u) = 0.
-1, -1/2, 0, 2, 4
Suppose -v - 4 = 5*n + 10, -4*v + 8 = 4*n. Let g = 0 + v. Factor -6 + 10*y - 19*y + 3*y**2 + g*y.
3*(y - 2)*(y + 1)
Let o(f) be the first derivative of f**6/1080 + f**5/90 + f**4/18 - 19*f**3/3 + 30. Let k(d) be the third derivative of o(d). Solve k(z) = 0 for z.
-2
Let b(v) be the third derivative of -v**5/180 - v**4/12 - 5*v**3/18 + v**2 - 96. Determine a, given that b(a) = 0.
-5, -1
Let u(f) = 29*f + f**2 + 5*f**3 + 1 + 7 - 6*f**2 + 5. Suppose 0 = 3*o + 41 - 2. Let x(j) = 2*j**3 