3*w - 4/3*w**5 - 28/3*w**4 - 24*w**3.
-4*w*(w + 1)*(w + 2)**3/3
Factor 9/2*j**3 + 27/4*j**2 - 3*j + 3/4*j**4 - 9.
3*(j - 1)*(j + 2)**2*(j + 3)/4
Let i(d) be the first derivative of -3/11*d**2 + 10/33*d**3 + 0*d + 1. Factor i(s).
2*s*(5*s - 3)/11
Let r(w) be the first derivative of -w**4/12 + 2*w**3/9 - 71. Solve r(b) = 0.
0, 2
What is p in p**2 + 2*p**3 + 21*p**2 - 3*p - 17 + 11*p**2 + p**3 - 16 = 0?
-11, -1, 1
Factor -8/11*c**2 - 16/11*c + 2/11*c**4 + 0 + 4/11*c**3.
2*c*(c - 2)*(c + 2)**2/11
Determine a so that -2/7*a**4 - 8/7 + 0*a**3 + 10/7*a**2 + 0*a = 0.
-2, -1, 1, 2
Let g(y) be the third derivative of -11*y**8/2016 - 5*y**7/252 + 3*y**6/80 + 53*y**5/360 - 2*y**4/9 - y**3/3 + 36*y**2 + y. Find c, given that g(c) = 0.
-2, -3/11, 1
Let j(g) be the first derivative of -23 + 29/10*g**2 - 3/5*g**3 - 6/5*g. Factor j(w).
-(w - 3)*(9*w - 2)/5
Let x(b) be the first derivative of -b**7/210 + b**5/20 - 2*b**3/15 + 44*b + 1. Let w(a) be the first derivative of x(a). Let w(h) = 0. What is h?
-2, -1, 0, 1, 2
Let u(q) = -q**3 - q - 1. Let t(y) = -38*y**3 - 84*y**2 - 46*y - 2. Let l(f) = t(f) + 2*u(f). Factor l(m).
-4*(m + 1)**2*(10*m + 1)
Let o be -3 + 27 + 1 + 3. Suppose 18*m**2 - o*m**2 - 25*m - 15*m + 5*m**2 = 0. Calculate m.
-8, 0
Let s(f) be the first derivative of f**6/195 - f**5/130 - 25*f - 6. Let x(w) be the first derivative of s(w). Suppose x(u) = 0. What is u?
0, 1
Let o(w) be the first derivative of -4*w**2 - 6*w - 16 - 2/3*w**3. Factor o(h).
-2*(h + 1)*(h + 3)
Let b(z) be the third derivative of 55/24*z**4 - 1/4*z**5 + 0*z - 5*z**3 + 5*z**2 + 0. Solve b(n) = 0.
2/3, 3
Let z be (-1)/6 + 3/9. Let s(c) be the second derivative of z*c**3 + 1/6*c**4 + 0*c**2 + 0*c**5 - 5*c - 1/42*c**7 - 1/15*c**6 + 0. What is r in s(r) = 0?
-1, 0, 1
Let p(i) be the first derivative of i**5/10 - 7*i**3/6 - 3*i**2/2 - 21. Let p(z) = 0. What is z?
-2, -1, 0, 3
Let w(c) be the third derivative of c**8/420 + c**7/210 - c**6/90 - c**5/30 - 16*c**3/3 - 33*c**2. Let d(b) be the first derivative of w(b). Factor d(x).
4*x*(x - 1)*(x + 1)**2
Let i(a) be the third derivative of a**8/672 - 11*a**7/420 + 43*a**6/240 - 73*a**5/120 + 7*a**4/6 - 4*a**3/3 + 267*a**2. Determine c, given that i(c) = 0.
1, 4
Factor 6/5*x**2 - 9/5*x + 4/5 - 1/5*x**3.
-(x - 4)*(x - 1)**2/5
Let y = 6/3353 + 10035/13412. Let 9/2*t**4 - 3/2*t**2 + 0 - 27/8*t**5 + y*t**3 - 3/8*t = 0. What is t?
-1/3, 0, 1
Let o(i) be the first derivative of 25*i**6/48 - 5*i**5/8 - i**4/8 + i**3/6 - 26. Solve o(y) = 0 for y.
-2/5, 0, 2/5, 1
Let s(y) be the first derivative of 0*y + 5/8*y**4 + 1/2*y**3 + 3/2*y**2 + 5 + 1/5*y**5. Let h(m) be the second derivative of s(m). Suppose h(i) = 0. What is i?
-1, -1/4
Let k(c) be the second derivative of 0*c**2 - 1/30*c**5 + 0*c**4 + c**3 + 4*c + 0 - 1/180*c**6. Let n(s) be the second derivative of k(s). Factor n(i).
-2*i*(i + 2)
Let q(m) be the second derivative of -m**7/5040 - m**6/720 - m**5/240 - 11*m**4/6 + 7*m. Let c(i) be the third derivative of q(i). Let c(j) = 0. What is j?
-1
Let v = 11 + -3. Suppose v*y = 10*y - 8. Factor -9*i - 11*i + y*i**2 + 8*i + 8.
4*(i - 2)*(i - 1)
Let j(d) be the second derivative of d**6/75 + 3*d**5/50 + d**4/30 - d**3/5 - 2*d**2/5 - 96*d. Factor j(s).
2*(s - 1)*(s + 1)**2*(s + 2)/5
Let f = 20 - 15. Let k be (36/(-30))/((-2)/f). Find r, given that -21*r + 47*r**k - 65*r**3 + 7*r + 30*r**2 + 2 = 0.
1/3, 1
Solve 14/3*x**2 - 11/3*x + 0 - x**3 = 0.
0, 1, 11/3
Let p(l) be the second derivative of l**5/480 + 7*l**4/192 - l**2 + 11*l. Let h(m) be the first derivative of p(m). Factor h(o).
o*(o + 7)/8
Factor 65/4*o - 20*o**2 + 5/4*o**3 + 75/2.
5*(o - 15)*(o - 2)*(o + 1)/4
Let w(h) = -h**2 + 28*h + 258. Let y(g) = 2*g**2 - 26*g - 259. Let l(k) = 3*w(k) + 2*y(k). Factor l(t).
(t + 16)**2
Let a(g) be the third derivative of -g**5/270 + 7*g**4/36 - 80*g**3/27 - g**2 + 653*g. What is c in a(c) = 0?
5, 16
Let s(r) = 22*r**2 - 7*r - 6. Let g(v) = -87*v**2 + 27*v + 27. Let a(x) = 2*g(x) + 9*s(x). Find o, given that a(o) = 0.
0, 3/8
Let a be -2180*(-25)/18500 - (-4)/74. Solve 0 + 7/5*i**2 + 8/5*i - 1/5*i**a = 0 for i.
-1, 0, 8
Let t(n) be the first derivative of -32*n**3/3 - 38*n**2 - 24*n - 795. Solve t(w) = 0.
-2, -3/8
Find i, given that -3*i**3 - 39/4*i**2 - 21/2*i - 15/4 = 0.
-5/4, -1
Let m be 2790/75 - 11 - 7/1. Factor 2/5*h**3 - 72/5 - 26/5*h**2 + m*h.
2*(h - 6)**2*(h - 1)/5
Let o(j) = -j + 10. Suppose 33 = 4*q + 5. Let g be o(q). Let 3*h + 6*h**3 - 3*h**g + 3*h + 0*h**2 - 9*h**2 = 0. What is h?
0, 1, 2
Suppose -11*t = -16*t + 405. Let w be (18/t)/(1 - (-1 + 1)). Determine a, given that -14/9*a**3 + 16/9*a + 10/9*a**4 - 2/9*a**5 - 8/9 - w*a**2 = 0.
-1, 1, 2
Let b be ((92/(-161))/4)/(-1 - (-12)/16). Factor 0*t**2 - 6/7*t + 2/7*t**3 + b.
2*(t - 1)**2*(t + 2)/7
Let u(g) be the first derivative of -g**6/2 - 3*g**5 + 15*g**4/4 + 25*g**3 - 60*g**2 + 48*g - 51. Factor u(q).
-3*(q - 1)**3*(q + 4)**2
Let f(x) be the third derivative of x**6/270 - x**5/135 - x**4/9 + 40*x**2 - x. Factor f(u).
4*u*(u - 3)*(u + 2)/9
Let y be 9*(120/(-18))/5. Let t be (4/(-14))/(8/y). Factor -48/7 - 24/7*r - t*r**2.
-3*(r + 4)**2/7
Let t = -30350 - -30353. Solve 0 + 0*s**2 - 5/3*s**t + 0*s + 1/3*s**4 = 0.
0, 5
Let k = 1/1713 - -1141/1713. Let y be (-26)/(-15) + (-4)/10. Factor -2/3*t - 2*t**2 + y + 2/3*t**3 + k*t**4.
2*(t - 1)**2*(t + 1)*(t + 2)/3
Let v = 941 - 936. Let g(c) be the second derivative of 9*c + 0 - 1/3*c**3 + 2*c**2 + 1/10*c**v - 1/3*c**4. Factor g(f).
2*(f - 2)*(f - 1)*(f + 1)
Find g, given that 8/3 + 0*g + 2/3*g**3 - 2/3*g**5 - 14/3*g**2 + 2*g**4 = 0.
-1, 1, 2
Let j(z) be the first derivative of -z**5/25 + 19*z**4/20 - 38*z**3/5 + 112*z**2/5 - 128*z/5 - 40. Factor j(o).
-(o - 8)**2*(o - 2)*(o - 1)/5
Let k(a) = -a**4 + a**3 - 6*a**2 - 2*a + 2. Let t(p) = 0*p**3 - 20*p**2 - 3*p + 14*p**2 + 3 + 2*p**3 + 0 - 2*p**4. Let s(d) = 6*k(d) - 4*t(d). Factor s(b).
2*b**2*(b - 3)*(b + 2)
Let p(g) = 23 - 48*g - 48*g**2 + 9 - 52. Let z(v) = -7*v**2 - 7*v - 3. Let j(c) = 3*p(c) - 20*z(c). Solve j(i) = 0.
-1, 0
Let c(y) = 2*y**5 + 8*y**4 - 5*y**3 - 15*y**2 - 5. Let x(h) = -3*h**5 - 12*h**4 + 8*h**3 + 24*h**2 + 8. Let j(k) = 8*c(k) + 5*x(k). Suppose j(r) = 0. What is r?
-4, 0
Suppose -3/4 + 3/4*q**2 - 3/4*q + 3/4*q**3 = 0. What is q?
-1, 1
Let b(d) = -d**2 + 183*d + 363. Let u(c) = -c**2 + 91*c + 183. Let k(m) = 3*b(m) - 7*u(m). Factor k(h).
4*(h - 24)*(h + 2)
Let t = 1533 + -4552/3. Let q = -15 + t. Let q + 10/3*u**2 - 4*u = 0. Calculate u.
1/5, 1
Let l(b) be the third derivative of 0 + 0*b + 1/180*b**5 + 2*b**3 - 6*b**2 + 1/6*b**4. Factor l(c).
(c + 6)**2/3
Let n(z) be the third derivative of -z**7/2100 - z**6/450 + 19*z**3/6 + 10*z**2. Let s(b) be the first derivative of n(b). Suppose s(j) = 0. What is j?
-2, 0
Let z(w) be the third derivative of w**5/150 + w**4/8 - 9*w**3/10 + 145*w**2 + 1. Factor z(p).
(p + 9)*(2*p - 3)/5
Let d be ((-4)/(-6))/((-6)/(-126)). Factor 13*z - 58*z - 120*z**2 - 53*z**3 - d*z**3 - 13*z**3 - 5.
-5*(z + 1)*(4*z + 1)**2
Solve -1/7*q**4 + 1/7*q**2 - 10/7*q + 10/7*q**3 + 0 = 0.
-1, 0, 1, 10
Suppose 7*h - 56 = -h. Let b(u) = 10*u**2 + 4*u - 13. Let w(i) = 7*i**2 + 3*i - 9. Let f(a) = h*w(a) - 5*b(a). Solve f(m) = 0 for m.
-1, 2
Suppose -58*d = -62*d + 104. Suppose 12*o - d*o = -28. Factor 0*m - 2/3*m**o + 0 - 2/3*m**3.
-2*m**2*(m + 1)/3
Let d = 2/2921 + 2909/17526. Suppose -2/3*u + d*u**5 + 4/3*u**2 - 1/2*u**3 - 1/3*u**4 + 0 = 0. Calculate u.
-2, 0, 1, 2
Suppose l + 4*i + 8 = -i, l = -i. Factor 9*m**3 + 7 - 2*m**4 + 5*m**2 + 5*m**l - 3*m**3 - 15 - 6*m.
-2*(m - 4)*(m - 1)*(m + 1)**2
Factor 231/2*k**2 - 150 + 9/4*k**3 + 147*k.
3*(k + 2)*(k + 50)*(3*k - 2)/4
Let g(d) = -d**2 + 2. Let x be g(-1). Let n be (x - (-6)/(-8))/((-3)/(-6)). Factor n - 1/2*k**2 - 1/2*k + 1/2*k**3.
(k - 1)**2*(k + 1)/2
Let g be -3 - (1/(-3) + 42/(-9)). Factor -21*p + 6*p**g + 105*p**3 + 11 - 102*p**3 + 1.
3*(p - 1)**2*(p + 4)
Let u(n) be the second derivative of n**4/30 - 68*n**3/5 + 10404*n**2/5 - 9*n - 39. Factor u(i).
2*(i - 102)**2/5
Let c be ((-8)/3)/((-3)/(-9)). Let i = c - -11. Factor 0*a**3 - 3*a**i - 16*a**4 + 19*a**4.
3*a**3*(a - 1)
Let z = -716 - -4297/6. Factor -1/2*g**2 - z*g + 1/6*g**3 + 1/2.
(g - 3)*(g - 1)*(g + 1)/6
Let u(d) be the third derivative of -1/90*d**5 - 5/36*d**4