3*m**2 + 8/3*m = 0.
0, 2
Let b(j) be the second derivative of 1/15*j**4 + 0 + 5*j + 1/15*j**3 - 1/75*j**6 - 1/25*j**5 + 1/105*j**7 - 1/5*j**2. Find k, given that b(k) = 0.
-1, 1
Let h(m) be the first derivative of 27*m**4/4 - 2*m**3 - 27*m**2/2 + 6*m - 5. Let h(p) = 0. Calculate p.
-1, 2/9, 1
Suppose -10*y + 12*y = 10. Let l = -6 + 8. Find p, given that -5*p**4 + 11*p**4 + p**2 + l*p**3 - y*p**4 = 0.
-1, 0
Let a(j) be the first derivative of -4*j**5/15 - 7*j**4/6 - 8*j**3/9 + 4*j**2/3 + 8. Determine m, given that a(m) = 0.
-2, 0, 1/2
Suppose 5*f - 4*n + 18 = 7*f, 4*n = 4*f. What is x in -2/3*x + 1/3*x**2 + x**f + 0 = 0?
-1, 0, 2/3
Let j(d) be the first derivative of d**4/7 + 5*d**3/7 + 6*d**2/7 - 4*d/7 + 7. Factor j(n).
(n + 2)**2*(4*n - 1)/7
Let a = -135/14 + 71/7. Factor 1/2 + a*i**2 + i.
(i + 1)**2/2
Let b(n) be the third derivative of -1/15*n**7 - 11/30*n**5 + 1/6*n**4 + 0*n + 0 + 4/15*n**6 - 4*n**2 + 0*n**3. Factor b(u).
-2*u*(u - 1)**2*(7*u - 2)
Let f(n) be the first derivative of 2*n**6/3 + 8*n**5/5 + n**4 + 12. Let f(a) = 0. Calculate a.
-1, 0
Find z, given that -1/5*z + 3/5*z**3 - 4/5*z**2 + 2/5 = 0.
-2/3, 1
Let u(o) = o**2 + o - 1. Let z(v) be the third derivative of 7*v**5/60 + 5*v**4/12 - 4*v**3/3 - v**2. Let w(s) = -24*u(s) + 3*z(s). Solve w(n) = 0 for n.
0, 2
Let t(x) be the first derivative of -x**4/72 - x**3/36 + x**2/6 - 3*x - 2. Let a(f) be the first derivative of t(f). Factor a(c).
-(c - 1)*(c + 2)/6
Let f be (5 - (-155)/(-35)) + (-2)/7. Let 4/7*p**2 - 2/7*p - f = 0. What is p?
-1/2, 1
Let q(p) be the second derivative of -p**7/70 + 4*p**6/25 - 33*p**5/50 + 7*p**4/5 - 17*p**3/10 + 6*p**2/5 + 12*p. Find y, given that q(y) = 0.
1, 4
Let n be 7 - (4 - 4)/3. Let i(q) be the second derivative of 0*q**2 + 1/21*q**n + 0*q**3 + 0*q**4 + 4/15*q**6 + 2/5*q**5 + 0 + q. Determine t so that i(t) = 0.
-2, 0
Factor -2/15*r**5 - 4/15*r - 14/15*r**2 - 2/3*r**4 - 6/5*r**3 + 0.
-2*r*(r + 1)**3*(r + 2)/15
Let j = 1/117732 + 6534041/10007220. Let c = 5/34 + j. Factor -2/5*b + 0 - 2/5*b**3 - c*b**2.
-2*b*(b + 1)**2/5
Suppose -f + 12 = f - 3*g, 2*g + 10 = 2*f. Let p = 5 - f. Factor -2/3*t - 1/3 - 1/3*t**p.
-(t + 1)**2/3
Factor -78*b**5 + b**3 - b + 0*b + 77*b**5 + b**3.
-b*(b - 1)**2*(b + 1)**2
Let j(n) be the first derivative of -3*n**5/35 + 9*n**4/14 - n**3/7 - 36*n**2/7 - 48*n/7 - 9. Let j(o) = 0. What is o?
-1, 4
Let x(u) be the third derivative of u**6/60 - 2*u**5/15 + u**4/3 + 4*u**2. Factor x(y).
2*y*(y - 2)**2
Let v(r) be the first derivative of r**5 + 5*r**4/2 - 5*r**2 - 5*r - 8. Factor v(y).
5*(y - 1)*(y + 1)**3
Suppose -2*h - 6 = -4*h. Let v(t) be the third derivative of 1/70*t**7 + t**2 - 1/60*t**5 + 0 - 1/60*t**6 + 0*t**4 + 0*t**h + 0*t. Factor v(s).
s**2*(s - 1)*(3*s + 1)
Let t(d) = 11*d**2 + d - 5. Let n(a) = 6*a**2 - 2. Let s(r) = -7*n(r) + 4*t(r). Factor s(j).
2*(j - 1)*(j + 3)
Let q(o) = -3*o + 3. Let p be q(5). Let t be (-20)/p - 2/2. Let -t*k**3 + 4/3*k**2 - 2/3*k + 0 = 0. Calculate k.
0, 1
What is b in 1/6*b**3 + 2/3*b**2 + 5/6*b + 1/3 = 0?
-2, -1
Let d be (-8)/(-2) + -9 + 6. Let j be d - (-8)/18 - 1. Factor j - 2/9*y**3 + 2/9*y - 4/9*y**2.
-2*(y - 1)*(y + 1)*(y + 2)/9
Let y(x) be the first derivative of -3*x**6/7 + 12*x**5/7 - 2*x**4 + 16*x**3/21 - 4. Factor y(g).
-2*g**2*(g - 2)*(3*g - 2)**2/7
Determine g, given that 20/7*g**3 + 0 + 16/7*g + 34/7*g**2 + 2/7*g**4 = 0.
-8, -1, 0
Let i(w) = w**4 - w**3 - w + 1. Let m(j) = 6*j**4 - 2*j**3 + 2*j**2 - 5*j + 5. Let c(s) = -10*i(s) + 2*m(s). Factor c(a).
2*a**2*(a + 1)*(a + 2)
Let l(d) be the first derivative of -4*d**3/3 - 2*d**2 + 8*d + 23. Factor l(p).
-4*(p - 1)*(p + 2)
Let r be ((-4)/7)/((-30)/105). Let f be ((8/(-7))/(-2))/r. Factor 2/7*u - f*u**3 + 0 + 0*u**2.
-2*u*(u - 1)*(u + 1)/7
Let i(d) be the second derivative of 0 + 1/273*d**7 + 0*d**3 + 1/65*d**6 - 7/78*d**4 + d - 1/130*d**5 + 4/13*d**2. Let i(b) = 0. What is b?
-2, -1, 1
Let s(j) = -85*j**4 + 155*j**3 - 85*j**2 - 180*j + 120. Let a(u) = 7*u**4 - 13*u**3 + 7*u**2 + 15*u - 10. Let y(i) = 25*a(i) + 2*s(i). What is c in y(c) = 0?
-1, 1, 2
Let l(d) be the second derivative of d**7/273 + 2*d**6/195 - d**5/130 - d**4/39 - 3*d. Suppose l(r) = 0. Calculate r.
-2, -1, 0, 1
Let g = -14 + 34. Suppose y = -4*y + d + 4, 3*y - g = 5*d. Factor 1/2*c**2 + y - c + 1/2*c**3.
c*(c - 1)*(c + 2)/2
Let c(s) be the first derivative of 2*s**3/3 + s**2 - 4*s + 6. Determine x, given that c(x) = 0.
-2, 1
Suppose -2*m + 4*m = 10. Suppose 6*o - m = o - 5*z, 2*o - z - 5 = 0. Factor 0 - 2/7*l + 4/7*l**o - 2/7*l**3.
-2*l*(l - 1)**2/7
Let j = -12/13 + 86/65. Let j*k**2 + 2/5 + 4/5*k = 0. What is k?
-1
Let l = -16/23 + 218/115. Factor -3/5*q**4 - 6/5*q + l*q**3 + 3/5*q**2 + 0.
-3*q*(q - 2)*(q - 1)*(q + 1)/5
Factor 8*y - y**3 - 17*y**2 + y**3 - y**4 + 6*y**3 + 5*y**2.
-y*(y - 2)**3
Let u(g) be the third derivative of -g**8/84 - 2*g**7/21 - 29*g**6/120 - 4*g**5/15 - g**4/8 - 4*g**2. Determine w, given that u(w) = 0.
-3, -1, -1/2, 0
Suppose 2*x + 5*i = -8 + 17, 63 = 5*x - i. Suppose -2*l - 4*l = -x. Factor 0 - p + 5/2*p**l - 2*p**3 + 1/2*p**4.
p*(p - 2)*(p - 1)**2/2
Let b = -9521/9 + 1059. Suppose 0 = 2*c - 7*c - 5*l + 25, -l = 2*c - 8. Factor -4/9*t + 0 + 2/3*t**c + b*t**2.
2*t*(t + 2)*(3*t - 1)/9
Let m(q) = 4*q - 4. Let s(l) = l**2 - 3*l - 8. Let p be s(5). Let w be m(p). Factor 0*j + 4/5*j**2 + 2*j**w - 14/5*j**3 + 0.
2*j**2*(j - 1)*(5*j - 2)/5
Suppose 0 = 4*z + 3*o - 7*o, 15 = 5*o. Suppose 0 = z*w + 2*w. What is v in 1/2*v**2 + 0 + 1/2*v**4 - v**3 + w*v = 0?
0, 1
Let l(s) be the third derivative of s**7/105 + s**6/20 + s**5/15 + 6*s**2. Solve l(z) = 0.
-2, -1, 0
Let s = 42 - 124/3. Factor -s*v**3 - 2/3*v**2 + 0 - 2/9*v**4 - 2/9*v.
-2*v*(v + 1)**3/9
Let l(b) = -7*b**2 - 2*b + 4. Let g(p) = -p**2 - 7*p + 6. Let s be g(-7). Let j(t) = 8*t**2 + 3*t - 5. Let v(f) = s*l(f) + 5*j(f). Factor v(u).
-(u - 1)*(2*u - 1)
Suppose 10*p - 2*h = 6*p + 10, -p + 4*h = 8. Suppose 0*w + 1/2*w**2 + 0*w**3 - 1/4*w**p - 1/4 = 0. Calculate w.
-1, 1
Let f = 385 - 8063/21. Let w = f - 8/21. Factor w + 2/3*k**2 - 4/3*k.
2*(k - 1)**2/3
Let d(a) be the third derivative of a**8/20160 - a**7/5040 - a**6/360 + a**5/60 - a**2. Let c(i) be the third derivative of d(i). Solve c(u) = 0 for u.
-1, 2
Let u = -27 - -63. Let s be ((-27)/u)/(18/(-16)). Factor 0*m + 0 - s*m**4 - 4/3*m**3 - 2/3*m**2.
-2*m**2*(m + 1)**2/3
Let x(z) = 9*z**3 + 5*z**2 - 37*z + 1. Let j(f) = -5*f**3 - 2*f**2 + 19*f. Let p(t) = 11*j(t) + 6*x(t). Solve p(r) = 0.
1, 6
Let s(g) be the third derivative of 2*g**7/35 + g**6/15 - 4*g**5/15 - g**4/3 + 2*g**3/3 - 5*g**2. Factor s(q).
4*(q - 1)*(q + 1)**2*(3*q - 1)
Solve -4*x**5 + 9*x**2 + 12*x**3 - 4*x**4 + 11*x**2 - 6*x + 14*x = 0 for x.
-1, 0, 2
Let o(v) be the second derivative of -v**5/40 - v**4/12 + v**3/12 + v**2/2 - 8*v. Find u, given that o(u) = 0.
-2, -1, 1
Suppose 3*b + 5 = -8*w + 3*w, -4*b - 10 = 5*w. Let 6/11*k**w + 0 - 2/11*k + 2/11*k**4 - 6/11*k**3 = 0. Calculate k.
0, 1
Let -24/11*u**3 - 2/11*u**5 - 12/11*u**4 - 20/11*u**2 - 6/11*u + 0 = 0. Calculate u.
-3, -1, 0
Let b = 1/555 + 998/555. Let o = -139 + 698/5. Factor -b*u**3 + o*u**5 - 3*u**2 - 6/5*u + 3/5*u**4 + 0.
3*u*(u - 2)*(u + 1)**3/5
Let c be 48 + -46 - 22/14. Let -c*z**2 + 3/7*z**4 - 3/7*z**5 + 0 + 0*z + 3/7*z**3 = 0. Calculate z.
-1, 0, 1
Let s(j) be the third derivative of -j**11/1164240 + j**10/264600 - j**9/211680 + j**5/20 + 3*j**2. Let h(x) be the third derivative of s(x). Factor h(q).
-2*q**3*(q - 1)**2/7
Factor 15*q - 5*q**4 + 106*q**3 - 10 - 10 - 121*q**3 + 25*q**2.
-5*(q - 1)**2*(q + 1)*(q + 4)
Let f(p) be the second derivative of 3/10*p**5 + 1/10*p**6 - 5*p + 0*p**2 - 1/4*p**4 + 0 - p**3. Factor f(j).
3*j*(j - 1)*(j + 1)*(j + 2)
Let n be ((-8)/(-36))/(2 + (-8)/6). Factor -1/3*v + n*v**4 + 2/3 + 1/3*v**3 - v**2.
(v - 1)**2*(v + 1)*(v + 2)/3
Suppose -5*w = -10*w + f + 2, -w - 2*f - 4 = 0. Suppose -5*h + 2 = 2*x, -13 = 3*h + 4*x - 3. Let 1/3*p + 1/3*p**3 + w - 2/3*p**h = 0. What is p?
0, 1
Let w(v) = 5*v**3 + 62*v**2 + 107*v + 48. Let z(f) = -5*f**3 - 63*f**2 - 108*f - 47. Let y(k) = -3*w(k) - 2*z(k). Factor y(l).
-5*(l + 1)**2*(l + 10)
Let t(n) be the second derivative of n**6/10 - n**4/2 + 3*n**2/2 + 41*n. Factor t(d).
3*(d - 1)**2*(d + 1)**2
Let l(b) = 39*b**3 - 126*b**2 + 270*b - 150. L