 4*p**5/75 + 11*p**4/30 - 4*p**3 - 494*p**2. Factor h(y).
-4*(y - 5)*(y - 2)*(y + 3)/5
Let c(u) be the second derivative of u**7/63 + 19*u**6/180 - u**5/24 - 1387*u + 1. Factor c(q).
q**3*(q + 5)*(4*q - 1)/6
Let d(m) be the third derivative of -m**6/18 - 4*m**5/15 + 13*m**4/6 - 287*m**3/6 - 22*m**2 - 1. Let p(s) be the first derivative of d(s). Factor p(c).
-4*(c - 1)*(5*c + 13)
Let j(b) be the third derivative of b**7/1995 - 89*b**6/570 + 6781*b**5/570 + 445*b**4 + 5700*b**3 + b**2 + 1512. Solve j(o) = 0.
-6, 95
Factor 855 + 3/2*i**3 - 1851/2*i + 69*i**2.
3*(i - 10)*(i - 1)*(i + 57)/2
Let d(c) be the second derivative of c**7/105 - c**6/15 - 24*c**5/25 + 18*c**4/5 + 2814*c. Suppose d(w) = 0. What is w?
-6, 0, 2, 9
Let y(u) be the first derivative of -5*u**6/6 - 32*u**5 + 5*u**4/4 + 160*u**3/3 + 719. Find f, given that y(f) = 0.
-32, -1, 0, 1
Let s(b) be the second derivative of 8/5*b**5 + 99 - 61/105*b**6 - 16/21*b**3 - 22/21*b**4 + 0*b**2 - b + 3/49*b**7. Let s(o) = 0. What is o?
-2/9, 0, 1, 2, 4
Let v(s) = -3*s + 28. Let g be v(8). Suppose -35*m**5 - 60*m**g - 13 + 3 - 25*m**2 + 15*m + 95*m**2 + 20*m**3 = 0. What is m?
-1, 2/7, 1
Let 10/9*k**4 - 2/9*k**5 + 0 + 20/9*k - 34/9*k**2 + 2/3*k**3 = 0. Calculate k.
-2, 0, 1, 5
Let p be 3*(60/56 + 51/(-714)). Let -1/8*w**p - 9261 - 1323/2*w - 63/4*w**2 = 0. Calculate w.
-42
Factor -1434672/5*s + 1259712 + 36612/5*s**2 - 329/5*s**3 + 1/5*s**4.
(s - 108)**3*(s - 5)/5
Suppose -2*c - 3*c = -2*j - 21, 4*c - 21 = 3*j. Suppose -2*r = -5*r - 12, -2*o = c*r + 8. Suppose 2/11 - 2/11*y**o + 6/11*y - 6/11*y**3 = 0. What is y?
-1, -1/3, 1
Let k(l) be the second derivative of -5*l**4/6 - 107*l**3/3 - 42*l**2 - 11*l + 2. Determine g, given that k(g) = 0.
-21, -2/5
Suppose -2*p - 26 = -4*n, 8 = 2*n + 6*p - 2*p. Suppose 3*g = -0*g + n. Factor 0*t**g - 2*t**2 - 4*t**3 + t**3 + 2*t**3.
-t**2*(t + 2)
Let v(i) = -5*i**2 + 44*i + 60. Let w be v(10). Factor 0 - 16/13*k**2 - 4/13*k**3 + 2/13*k**4 + w*k.
2*k**2*(k - 4)*(k + 2)/13
Let c(p) be the second derivative of -p**6/5 + 87*p**5/20 - 63*p**4/2 + 110*p**3 - 204*p**2 - 2*p + 3758. Determine k so that c(k) = 0.
2, 17/2
Let b(x) = -4*x**5 + 14*x**4 - 54*x**3 - 48*x**2 - 6*x + 12. Let t(k) = k**5 + 2*k**3 - k**2 + k - 2. Let h(i) = 2*b(i) + 12*t(i). Determine q so that h(q) = 0.
-9, -1, 0, 3
Let b be 182/(-1092) + 286/(-36) + 9. Factor 2450/9*d**2 + 280/9*d + b.
2*(35*d + 2)**2/9
Suppose g = 5*g - 2*p - 10, -p - 11 = -5*g. Let m(j) be the first derivative of 0*j**g + 1/4*j**4 + 0*j - 2/3*j**3 + 37 - 1/2*j**6 + 4/5*j**5. Factor m(c).
-c**2*(c - 1)**2*(3*c + 2)
Let w(p) = 16*p**3 - 1631*p**2 - 3265*p - 1633. Let b(t) = -9*t**3 + 816*t**2 + 1632*t + 816. Let a(z) = -5*b(z) - 3*w(z). Factor a(k).
-3*(k - 273)*(k + 1)**2
Suppose 3*t = -2*c - 21 + 27, 0 = 5*c - 15. Let d(p) be the second derivative of 0*p**2 + p + 3/20*p**5 + 0*p**3 - 1/30*p**6 + t - 1/6*p**4. Factor d(h).
-h**2*(h - 2)*(h - 1)
Let 13*v**3 + 1200 - 386376*v**2 + 1160*v + 386308*v**2 + 2*v**4 - 39*v**3 = 0. What is v?
-6, -1, 10
Let n(m) be the second derivative of m**5/10 + 155*m**4/6 + 166*m. Let n(r) = 0. Calculate r.
-155, 0
Let k(d) be the third derivative of -d**7/42 - 2*d**6/3 - 5*d**5/2 + 70*d**4/3 - 325*d**3/6 - 10*d**2 - 3*d. Find u such that k(u) = 0.
-13, -5, 1
Let b(z) be the third derivative of -z**8/448 - 23*z**7/280 - 7*z**6/20 + 49*z**5/4 - 1050*z**2. Factor b(r).
-3*r**2*(r - 5)*(r + 14)**2/4
Let n be ((-10)/90*0)/(46 + -49). Factor -9/2*z**4 + 2*z + 4*z**2 + n - 3/2*z**3.
-z*(z - 1)*(3*z + 2)**2/2
Let w(i) be the second derivative of -i**4/36 + 23*i**3/6 - 67*i**2/3 + 278*i. Factor w(p).
-(p - 67)*(p - 2)/3
Let -3475/7*a - 2250/7 + 1/7*a**5 - 198/7*a**3 - 2/7*a**4 - 1420/7*a**2 = 0. Calculate a.
-5, -1, 18
Let n(l) = 9*l**3 + 19*l**2 + 36*l + 21. Let i(m) = -4*m**3 - 10*m**2 - 18*m - 10. Let t = -25 + 30. Let x(b) = t*i(b) + 2*n(b). Solve x(v) = 0 for v.
-4, -1
Suppose -3*c = i - 34, 5*c + 2*i - i - 60 = 0. Suppose 3*l = 5 + 7. Determine f, given that -13*f**2 - c*f**2 + 28*f**2 - l*f = 0.
0, 2
Suppose 2*k - 225237 = 2*z - 225213, 53 = -2*k - 5*z. Solve k - 10/9*d + 1/9*d**2 = 0.
1, 9
Let s(a) be the second derivative of -a**7/63 - 4*a**6/9 - 17*a**5/10 - 14*a + 6. Determine p so that s(p) = 0.
-17, -3, 0
Let c(s) be the third derivative of -s**8/2016 + 7*s**6/720 - s**5/60 + 48*s**2. Let c(t) = 0. What is t?
-3, 0, 1, 2
Let c(y) be the first derivative of -274/33*y**3 - 36/11*y - 63/22*y**4 - 18/55*y**5 + 43 - 93/11*y**2. What is k in c(k) = 0?
-3, -2/3, -1/3
Let b(h) be the third derivative of 4*h**7/315 + 289*h**6/90 + 86881*h**5/360 + 80089*h**4/48 + 2*h**2 + 3*h - 42. Solve b(w) = 0.
-283/4, -3, 0
Suppose 341*y - 381*y = 0. Let s(w) be the second derivative of 0*w**2 + 30*w + 3*w**3 - 1/4*w**4 + y. Factor s(z).
-3*z*(z - 6)
Suppose 3*d - 4*g + 364 = 345, 4*d = -2*g + 26. Factor 6*i**2 - 2/3*i**d + 0 - 16/3*i.
-2*i*(i - 8)*(i - 1)/3
Factor 32/3 - 2*l - 1/6*l**2.
-(l - 4)*(l + 16)/6
Let j(o) be the third derivative of -o**8/336 + 29*o**7/210 - 8*o**2 - 60. Let j(k) = 0. What is k?
0, 29
Let g(j) be the third derivative of -j**7/42 + 7*j**6/2 - 199*j**5/6 + 95*j**4/2 + 1185*j**3/2 + 9088*j**2. Factor g(r).
-5*(r - 79)*(r - 3)**2*(r + 1)
Let o = 33 + -33. Suppose 3*r = -2*z, o = 2*r + 4*z + 7 + 1. Factor 6*d - 2*d + r*d**3 + 3 - 5*d**2 - 3 - 1.
(d - 1)**2*(2*d - 1)
Factor -3221*q**2 - 230*q + 224 + 1615*q**2 + 1602*q**2 + 10*q.
-4*(q - 1)*(q + 56)
Let z = 6919/69990 + 8/6999. Let v be (-62)/(-20) + 3/(-1). Factor v*j**4 + z*j**2 - 3/10*j**3 - 1/5 + 3/10*j.
(j - 2)*(j - 1)**2*(j + 1)/10
Let q(f) be the first derivative of f**3 + 2502*f**2 + 2086668*f - 844. Solve q(a) = 0.
-834
Let v(i) be the third derivative of i**7/1575 + i**6/225 + i**5/450 - i**4/30 - 32*i**2 + 15. Suppose v(d) = 0. Calculate d.
-3, -2, 0, 1
What is v in -104/11 + 86/11*v**2 - 96/11*v - 30/11*v**4 + 2/11*v**5 + 46/11*v**3 = 0?
-1, 2, 13
Suppose 2*v + 2 = 0, -4 = 2*g - g - 2*v. Let q be -5 - (6/12 + g). Factor 0 - 5/8*o**2 + 1/8*o**3 + q*o.
o*(o - 4)*(o - 1)/8
Let z = -858/29 - -7751/261. Let y(f) be the second derivative of -2/9*f**4 - z*f**3 + f + 0*f**2 + 1. Factor y(j).
-2*j*(4*j + 1)/3
Let y = 228 + -220. Factor -44*b + 80 + 14 - 12 + y + 20*b**2 - 91*b.
5*(b - 6)*(4*b - 3)
Let t(j) = -5*j**3 + 5*j**2 + 5*j - 5. Let a = -262 - -261. Let k(r) = r**3 - r**2 - r + 1. Let i(y) = a*t(y) - 4*k(y). Factor i(l).
(l - 1)**2*(l + 1)
Find y, given that 0 - 212/19*y**2 - 6/19*y**3 + 2/19*y**5 + 144/19*y + 72/19*y**4 = 0.
-36, -2, 0, 1
Let u = -328645 - -328726. Factor u*l - 792/5*l**2 - 51/5 - 48/5*l**3.
-3*(l + 17)*(4*l - 1)**2/5
Solve 5840/3*i + 5600 + 2/21*i**3 + 566/21*i**2 = 0.
-140, -3
Let p be ((-9)/(-150))/(945/525). Let l(m) be the first derivative of 3 - 4/15*m**3 - 2/5*m**2 - p*m**6 + 3/20*m**4 + 0*m + 2/25*m**5. Solve l(n) = 0 for n.
-1, 0, 2
Let c(l) = 2*l - 10. Let q(u) = 100*u**2 - 2056*u + 10589. Let f(n) = 6*c(n) - 3*q(n). Find z such that f(z) = 0.
103/10
Let n(k) be the first derivative of -97 + 12/7*k + 13/7*k**2 - 22/7*k**3. Find x, given that n(x) = 0.
-3/11, 2/3
Let u(c) = 16*c**4 - 110*c**3 + 105*c**2 + 101*c - 103. Let z(p) = 7*p**4 - 55*p**3 + 53*p**2 + 51*p - 52. Let q(l) = -4*u(l) + 9*z(l). Let q(g) = 0. What is g?
-56, -1, 1
Factor 2/11*z**3 - 358/11*z**2 - 1470 + 4718/11*z.
2*(z - 165)*(z - 7)**2/11
Let d be (43 - (-3720)/(-90)) + (-3)/2. Let l(b) be the first derivative of -b**2 + 2/3*b + 2/3*b**3 - d*b**4 - 21. Find s such that l(s) = 0.
1
Let a = 770 + -291. Find g, given that a*g - 8 - 495*g - 2*g**2 - 2*g**2 - 4 = 0.
-3, -1
Find k, given that -8/5*k + 0 - 26/15*k**2 + 0*k**3 + 2/15*k**4 = 0.
-3, -1, 0, 4
Let s = -54 - -57. Suppose -16*c + 13*c = -s. Factor q + 3 + 0 - q**2 + c - 2.
-(q - 2)*(q + 1)
Suppose 0 = 2*g + 2, 0 = -4*z + 2*g + 2. Let m be (8 + -7)*(25 - z). What is i in -4 + 3 - 2*i**2 + 27*i - m*i + i**2 = 0?
1
Factor 1285/2*y - 1/4*y**2 - 1651225/4.
-(y - 1285)**2/4
Let o(q) be the first derivative of 1/12*q**3 - 136 + 19/8*q**2 + 0*q. Suppose o(a) = 0. What is a?
-19, 0
Suppose 3*u + 11 = 5*c - 116, -c - u = -27. Factor 8*b**3 - 21*b**2 + 13*b**3 - 22*b**3 - 55*b - 44*b + c + 95.
-(b - 1)*(b + 11)**2
Let v = 76065/7 - 380129/35. Factor -64*d - 2/15*d**3 - 320/3 - v*d**2.
-2*(d + 2