0*u**2 + 106*u. Suppose i(z) = 0. What is z?
-5, -2
Let j(t) be the third derivative of -t**8/168 + 16*t**7/105 - 21*t**6/20 - 8*t**5/15 + 16*t**4/3 - 119*t**2 + 2*t. Solve j(v) = 0.
-1, 0, 1, 8
Let u(b) = -2*b**3 - 20*b**2 - 18*b + 3. Let t(n) = -3*n**3 - 41*n**2 - 38*n + 5. Let c(g) = -6*t(g) + 10*u(g). Factor c(s).
-2*s*(s - 24)*(s + 1)
Let t(c) = -4*c**4 - 8*c**3 + 4*c**2 + 11*c + 3. Let j = 23 + -26. Let x(z) = -4*z**4 - 8*z**3 + 4*z**2 + 12*z + 4. Let n(r) = j*x(r) + 4*t(r). Factor n(f).
-4*f*(f - 1)*(f + 1)*(f + 2)
Factor 54/17*j**3 + 0*j + 0 + 2/17*j**5 - 18/17*j**4 - 54/17*j**2.
2*j**2*(j - 3)**3/17
Let 64*a**3 + 8*a**2 - 33*a - 3*a + 1 + 7 - 16*a**4 - 28*a**3 = 0. Calculate a.
-1, 1/4, 1, 2
Let g(v) be the third derivative of 1/6*v**3 + 1/120*v**6 + 0*v - 1/60*v**5 - 4*v**2 - 1/24*v**4 + 0. Factor g(b).
(b - 1)**2*(b + 1)
Let v(u) = -5*u**2 - 360*u + 11528. Let i(c) = 33*c**2 + 2523*c - 80697. Let k(h) = -4*i(h) - 27*v(h). Solve k(d) = 0 for d.
62
Let l(u) be the first derivative of -u**5/180 + u**4/72 + u**3/9 + 15*u**2/2 + 14. Let v(b) be the second derivative of l(b). Let v(j) = 0. Calculate j.
-1, 2
Let q(d) be the second derivative of d**7/98 - d**6/35 + 3*d**5/140 - 179*d. Factor q(m).
3*m**3*(m - 1)**2/7
Let r(m) be the first derivative of 1/9*m**3 - m**2 + 16/15*m**5 + 21 + 1/3*m + 2*m**4. Find a such that r(a) = 0.
-1, 1/4
Let f be ((-1279)/3 + 1)*(-2)/(-8). Let k = 1483/12 + f. Factor k*p**2 - 15*p - 21/4*p**3 + 3.
-3*(p - 2)*(p - 1)*(7*p - 2)/4
Let x(s) = s - 1. Let g(v) = -6*v**3 - 40*v**2 - 65*v - 39. Let n(r) = 2*g(r) - 14*x(r). Factor n(c).
-4*(c + 2)*(c + 4)*(3*c + 2)
Factor -15*j**2 - 84 - 3/2*j**3 + 78*j.
-3*(j - 2)**2*(j + 14)/2
Let w(u) be the first derivative of 10 + 2*u**5 - 1/6*u**6 - 45/2*u**2 + 20*u**3 - 55/6*u**4 + 3*u. Let v(g) be the first derivative of w(g). Solve v(f) = 0.
1, 3
Solve 4*z**5 - 52*z**3 - 96*z**4 + 120*z**4 + 3*z + 48*z**2 - 19*z - 8*z**5 = 0 for z.
0, 1, 2
Let j be (-47070)/64575 + 2/(-14). Let q = -3/205 - j. Let -2/7*v**2 + 10/7*v - 2/7*v**3 - q = 0. What is v?
-3, 1
Let f = -1723 - -1726. Factor 0 + 2/9*u**f - 4/9*u**2 - 2/3*u.
2*u*(u - 3)*(u + 1)/9
Let o be ((-1824)/(-2040) - (-2)/(-2))*(-9 - 1). Suppose -54/17*w - 2/17*w**3 - 54/17 - o*w**2 = 0. What is w?
-3
Determine c, given that -8/7*c**2 + 4/7*c**4 + 4/7 - 2/7*c + 4/7*c**3 - 2/7*c**5 = 0.
-1, 1, 2
Let i(r) = 15*r**4 + 41*r**3 - 11*r**2 + 11*r. Let u(h) = 735*h**4 - 2*h**2 + 3*h + 8*h**3 - 732*h**4 - h. Let l(j) = 2*i(j) - 11*u(j). Factor l(b).
-3*b**3*(b + 2)
Let -2*o**2 + 24 + 3067*o - o**2 - 3046*o = 0. Calculate o.
-1, 8
Let j be -2 - 1*-3 - (6 + -8). Suppose j*m + 16 = 5*x + 4*m, 0 = 5*x + 2*m - 12. Find l, given that 0 + 1/3*l - 1/3*l**x + 1/3*l**2 - 1/3*l**3 = 0.
-1, 0, 1
Let -2040*w**3 - 1/7*w**5 + 98000*w + 44800*w**2 + 0 + 208/7*w**4 = 0. Calculate w.
-2, 0, 70
Let g(z) be the third derivative of z**7/280 + z**6/16 + 37*z**5/80 + 15*z**4/8 + 9*z**3/2 + 2*z**2 + 47*z. Factor g(b).
3*(b + 2)**2*(b + 3)**2/4
Let v = 46104 + -370071/8. Let z = v - -155. Find i such that 0*i**2 - z*i**3 + 3/8*i + 1/4 = 0.
-1, 2
Find v, given that v**2 - 117*v**3 + 55*v**3 - 5*v**2 + 6*v**5 + 56*v**3 + 4*v**4 = 0.
-1, -2/3, 0, 1
Let f(d) be the first derivative of -242*d**5/5 + 319*d**4/2 + 408*d**3 + 188*d**2 + 32*d - 168. Suppose f(v) = 0. Calculate v.
-1, -2/11, 4
Let f(z) be the second derivative of 3*z**5/20 + 7*z**4/20 + z**3/5 - 9*z. Factor f(c).
3*c*(c + 1)*(5*c + 2)/5
Let k be (9 - 14)*(1 - (3 + -1)). Solve -5 - k*f**2 + 9*f**2 + 5 + 4*f = 0.
-1, 0
Suppose 0*z + 12/5*z**3 + 9/5*z**2 + 3/5*z**4 + 0 = 0. Calculate z.
-3, -1, 0
Let q(f) be the first derivative of -f**3/21 - 3*f**2/7 + f - 51. What is d in q(d) = 0?
-7, 1
Determine n so that 80 - 40*n**2 - 1608*n**3 + 1593*n**3 + 50*n + 5*n**4 + 10*n = 0.
-2, -1, 2, 4
Suppose 6*z = 5*z. Let g be z + 0 - ((-44)/8)/11. What is q in g*q**2 - q**3 + 1/2*q**5 - 1/4*q**4 - 1/4 + 1/2*q = 0?
-1, 1/2, 1
Let i(t) be the first derivative of 0*t + 6*t**2 + 5 + 40/3*t**3 + 2/3*t**6 + 12*t**4 + 24/5*t**5. Suppose i(f) = 0. What is f?
-3, -1, 0
Let a(i) be the first derivative of -31 - 4*i**4 - 3*i**2 - 9*i**2 + 21 - 4*i - 12*i**3. Factor a(g).
-4*(g + 1)**2*(4*g + 1)
Let l = 1721 + -5218/3. Let b = -17 - l. Factor b*v**3 - 7/3*v - 5/3*v**2 + 2/3.
(v - 2)*(v + 1)*(4*v - 1)/3
Let a(k) be the second derivative of 0 - 23*k - k**2 + 1/2*k**3 + 0*k**4 - 1/20*k**5. Factor a(u).
-(u - 1)**2*(u + 2)
Let t = 0 + 0. Let p be 4/(-62) + ((-192)/248)/(-12). Determine m so that 0*m**2 - 2/5*m**5 + p*m + t + 0*m**4 + 2/5*m**3 = 0.
-1, 0, 1
Let a(q) = -q - 3. Let g be a(-7). Find h, given that 35*h**3 - 27*h**3 - 3*h**g + 4*h - 10*h**2 + h**4 = 0.
0, 1, 2
Let f(b) = b**2 - 8*b + 18. Let r be f(6). Let g be (-5*16/(-180))/(8/r). Determine t, given that 4/3*t + 1/3 + 2*t**2 + 4/3*t**3 + g*t**4 = 0.
-1
Let t = 2655 + -2653. Let -2/9*o**4 + 0*o + 4/9*o**t + 2/9*o**3 + 0 = 0. Calculate o.
-1, 0, 2
Suppose 17 = -8*p + 33. Let o(u) be the third derivative of -2*u**p + 1/180*u**6 + 0*u + 0 + 0*u**3 + 1/54*u**5 + 1/54*u**4. Factor o(y).
2*y*(y + 1)*(3*y + 2)/9
Let j(w) = -9*w**4 + 14*w**3 - 44*w**2 - 224*w + 872. Let g(x) = x**4 + x**2 + x - 1. Let i(a) = 40*g(a) + 5*j(a). Factor i(d).
-5*(d - 6)**3*(d + 4)
Suppose 216 + 2/3*o**4 - 18*o**2 - 72*o + 4*o**3 = 0. What is o?
-6, 3
Let c(v) be the second derivative of -3*v**5/70 - 4*v**4/21 - v**3/3 - 2*v**2/7 - 10*v + 12. Factor c(l).
-2*(l + 1)**2*(3*l + 2)/7
Let r(p) be the first derivative of p**6/3 + 24*p**5/5 + 18*p**4 - 28*p**3/3 - 165*p**2 - 252*p - 340. Determine j so that r(j) = 0.
-7, -3, -1, 2
Let k(m) be the first derivative of m**3/4 + 39*m**2/4 - 96. Suppose k(g) = 0. Calculate g.
-26, 0
Factor 10/7*f**2 + 48/7*f + 2/7*f**4 - 12/7*f**3 - 72/7.
2*(f - 3)**2*(f - 2)*(f + 2)/7
Let i = -3/20200 + 80821/141400. Factor -16/7*d + 2/7*d**4 - 8/7 - 6/7*d**2 + i*d**3.
2*(d - 2)*(d + 1)**2*(d + 2)/7
Let s = -16/71 + 167/426. Factor -s*h**4 + 1/6*h**5 - 1/2*h**3 + 1/6*h**2 + 0 + 1/3*h.
h*(h - 2)*(h - 1)*(h + 1)**2/6
Let k = -6317/7 + 903. Factor 4/7*a**2 + k + 8/7*a.
4*(a + 1)**2/7
Let r = -13 - -47. Solve -20*c - 3*c**2 + 3*c**3 + r*c - 20*c = 0 for c.
-1, 0, 2
Factor -39*w + 1521/2 + 1/2*w**2.
(w - 39)**2/2
Let a be (-175)/(-21) + 12*2/(-3). Factor -a + 1/6*g + 1/6*g**2.
(g - 1)*(g + 2)/6
Suppose 53*f - 55*f + 4 = 0. Factor 3/4*k + 9/4*k**3 + 0 + 3*k**f.
3*k*(k + 1)*(3*k + 1)/4
Factor -144 - 140*d**3 + 848*d + 48*d**2 - 687*d**2 - 525*d**2.
-4*(d + 9)*(5*d - 2)*(7*d - 2)
Suppose -3*o = -0*o + 2*r - 68, 2*o - 3*r = 54. Let m be 2/(-48)*9 - (-377)/o. Factor m*f - 66*f**2 - 90*f**4 - 4/3 + 126*f**3.
-2*(3*f - 1)**3*(5*f - 2)/3
Factor 168/13 + 2/13*n**3 + 256/13*n + 90/13*n**2.
2*(n + 1)*(n + 2)*(n + 42)/13
Let w(l) be the first derivative of 3*l**3/2 - 123*l**2/4 - 21*l - 13. Suppose w(a) = 0. Calculate a.
-1/3, 14
Let q(o) = 4*o**3 - 12*o**2 - 8*o + 6. Let t(v) = 17*v**3 - 50*v**2 - 31*v + 27. Let m(a) = -9*q(a) + 2*t(a). Find u, given that m(u) = 0.
-1, 0, 5
Let i = 1027/2 - 512. Let w(u) be the first derivative of i*u**2 - 3/2*u**3 + 0*u + 2. Determine d so that w(d) = 0.
0, 2/3
Let p(v) be the second derivative of -5/12*v**3 + 5/6*v**4 + 0*v**2 + 0 - 3/8*v**5 + 3*v. Determine n, given that p(n) = 0.
0, 1/3, 1
Let z be (-8)/6*(-1 - (-42)/(-12)). Let 12*v**2 + 3*v**3 - z*v**2 - v**3 + 4*v = 0. Calculate v.
-2, -1, 0
Let t(a) be the second derivative of -a**4/66 + 10*a**3/33 - 21*a**2/11 - 284*a. Factor t(b).
-2*(b - 7)*(b - 3)/11
Let i = 39/28 + 3/28. Let y(k) be the first derivative of k**3 - 3*k + 9 - i*k**2 + 3/4*k**4. Factor y(d).
3*(d - 1)*(d + 1)**2
Let q(z) be the third derivative of -z**6/480 - z**5/80 + 20*z**3/3 + 42*z**2. Let j(x) be the first derivative of q(x). Find m such that j(m) = 0.
-2, 0
Let u(o) = 20*o**2 + 264*o + 496. Let j(h) = -4*h**2 - 53*h - 99. Let s(t) = -16*j(t) - 3*u(t). Factor s(y).
4*(y + 2)*(y + 12)
Suppose 9/7*v**3 + 0 + 12/7*v**2 + 3/7*v = 0. What is v?
-1, -1/3, 0
Let v(x) = -x**2 - 14*x - 9. Let o(w) = 5*w**2 + 73*w + 46. Let l(r) = 2*o(r) + 11*v(r). Solve l(k) = 0 for k.
-7, -1
Suppose s + 15 = 9. Let c = s - -8. Factor -3/5*z**c - 9/5 + 12/5*z.
-3*(z - 3)*(z - 1)/5
Suppose 5*u + 61 - 1 = 0. Let t = u - -15. Factor 16 - 16*i - 3*i - 16*