
-2, -1, 1
Let g(f) be the first derivative of -4/21*f**3 + 12/35*f**5 - 12 - 4/7*f**2 + 4/7*f**4 + 0*f. Determine a, given that g(a) = 0.
-1, 0, 2/3
Let l(u) be the first derivative of 5*u**4 - 5/6*u**6 + 0*u**5 - 17 - 15/2*u**2 - 10/3*u**3 + 10*u. Find j, given that l(j) = 0.
-2, -1, 1
Let f(k) be the first derivative of -k**3/12 - 5*k**2/8 + 3*k/2 + 201. Find o such that f(o) = 0.
-6, 1
Factor 0*u + 0 + 2/5*u**4 - 2*u**3 + 0*u**2.
2*u**3*(u - 5)/5
Determine m, given that 0 + 3/5*m**5 - 12/5*m**2 - 8*m + 54/5*m**3 - 5*m**4 = 0.
-2/3, 0, 2, 5
Let t(h) = 2*h**3 + 10*h**2 - 3. Let i be t(-5). Let d(o) = 7*o + 23. Let v be d(i). Determine f so that 0 - 4/9*f**v + 4/9*f**3 - 4/9*f + 4/9*f**4 = 0.
-1, 0, 1
Let m(p) be the first derivative of -p**6/3 + 14*p**5/5 - 6*p**4 - 8*p**3/3 + 16*p**2 + 522. What is n in m(n) = 0?
-1, 0, 2, 4
Find o, given that -5/2*o**2 + 1/2*o**4 + 0*o + 0*o**3 + 2 = 0.
-2, -1, 1, 2
Let i(t) be the third derivative of 7*t**2 + 0 - 2/525*t**7 + 0*t + 0*t**4 + 0*t**5 + 1/840*t**8 + 0*t**3 + 1/300*t**6. Factor i(y).
2*y**3*(y - 1)**2/5
Let s(c) be the first derivative of -36/13*c - 34 + 3/13*c**2 + 8/39*c**3 - 1/26*c**4. Solve s(k) = 0.
-2, 3
Let b(u) = -4*u**2 - 154*u - 259. Let h(l) = -l**2 - 31*l - 52. Let r(j) = -2*b(j) + 11*h(j). Suppose r(x) = 0. What is x?
-9, -2
Let p be (-335)/(-45) - (-8)/(-18). Let c(u) be the first derivative of -3/2*u**4 - 9/5*u**5 + 2*u**3 + 9/2*u**2 - 1/2*u**6 - p + 3*u. Factor c(v).
-3*(v - 1)*(v + 1)**4
Let z(q) be the second derivative of -q**6/30 + 7*q**5/10 + 13*q**4/4 - 308*q**3/3 - 968*q**2 + 207*q. Factor z(i).
-(i - 11)**2*(i + 4)**2
Factor -726 + 3/2*j**3 + 129/2*j**2 + 660*j.
3*(j - 1)*(j + 22)**2/2
Let a(m) be the third derivative of -m**8/224 + m**7/20 - 61*m**6/360 + 11*m**5/90 + 7*m**4/18 - 8*m**3/9 + 467*m**2. Let a(w) = 0. Calculate w.
-2/3, 2/3, 1, 2, 4
Let r(w) be the second derivative of 2 - 10*w + 5/12*w**4 + 245/2*w**2 + 35/3*w**3. Factor r(b).
5*(b + 7)**2
Let c be (33/12)/(3/12). Suppose -8 = a - c. Factor -4*t**3 + 26*t**2 + 5*t**4 - 16*t**3 - t**2 - 7*t - a*t.
5*t*(t - 2)*(t - 1)**2
Let a(r) = -3*r**2 - r + 7. Let f(y) = -y**2 - y + 3. Let c be 5/(-50)*66 + (-2)/5. Let l(q) = c*f(q) + 3*a(q). Factor l(t).
-2*t*(t - 2)
Suppose -5*z + 2 = -v, 2*z + 4*v + 12 = 4. Let b(d) be the first derivative of 5 - 1/4*d**3 + z*d**2 + 3/4*d. Factor b(a).
-3*(a - 1)*(a + 1)/4
Let s(h) be the second derivative of -h**4/4 - h**3 + 8*h - 6. Find i, given that s(i) = 0.
-2, 0
Let o = -260111/5 + 52193. Let p = 171 - o. What is i in 1/5*i - 1/5*i**3 + 0 + 1/5*i**4 - p*i**2 = 0?
-1, 0, 1
Let k(z) be the first derivative of z**7/350 - z**6/200 + 23*z**2/2 - 2. Let l(t) be the second derivative of k(t). Solve l(b) = 0 for b.
0, 1
Let r(p) = p**3 + 5*p**2 - 3*p + 8. Let t be r(-6). Let z be 4/(-10) - (42/t)/7. Solve 0*i**3 + 0 + 0*i**2 - z*i**4 + 0*i = 0.
0
Factor 271*u - 158 + 5*u**4 + 70*u**3 + 260*u**2 + 59*u + 293.
5*(u + 1)**2*(u + 3)*(u + 9)
Let p(f) be the third derivative of -f**5/6 + 148*f**4/3 - 236*f**3/3 + 25*f**2 + 11*f. Factor p(m).
-2*(m - 118)*(5*m - 2)
Let z be -6 + (0 - -4) - -3. Let q be 12/30 + z/(-5). Factor 0*i**2 - q*i**4 + 0 - 3/5*i**3 + 4/5*i.
-i*(i - 1)*(i + 2)**2/5
Let s be (-2)/(-5)*40/16. Suppose 10 = -3*m + 4, 3*b + 5*m + s = 0. Factor -2*c**4 + 8*c**2 + c**2 + 2*c**3 - 3*c**2 + 1 - 5*c - 5*c**4 + b*c**5.
(c - 1)**3*(c + 1)*(3*c - 1)
Let g(a) = 8*a**2 - 18*a + 10. Let p(h) be the second derivative of -35*h**4/4 + 235*h**3/6 - 65*h**2 + 17*h. Let q(w) = -40*g(w) - 3*p(w). Solve q(j) = 0.
1, 2
Let z(l) be the third derivative of 0*l**3 + 3/40*l**6 + 0*l + 0 + 16*l**2 + 1/6*l**4 + 1/5*l**5. Factor z(j).
j*(3*j + 2)**2
Let a(l) = -l**4 + l**3 + l**2 - l + 6. Let r = 0 - 6. Let k(s) = -1. Let d(v) = r*k(v) - a(v). Let d(t) = 0. What is t?
-1, 0, 1
Suppose 5*n = 4*r - 7, 0 = 4*r - 5*r - n + 4. Suppose g = r*g + 4*z + 16, -5*g + z = -15. Factor 6/5*v**g + 2/5 - 8/5*v.
2*(v - 1)*(3*v - 1)/5
Factor 578*o**2 - 13*o**3 + 697*o**2 + 4*o**4 + 142*o**3 + 1125*o + 26*o**3 + o**4.
5*o*(o + 1)*(o + 15)**2
Let l = 506 + -2023/4. Factor -l*m + 1/4*m**2 - 1/2.
(m - 2)*(m + 1)/4
Let f(s) be the second derivative of 21*s**5/20 + 33*s**4/4 - 26*s**3 + 18*s**2 - s + 12. What is g in f(g) = 0?
-6, 2/7, 1
Let h = 8948 + -8948. Factor 0*j + 1/4*j**2 + h*j**3 + 0 - 1/4*j**4.
-j**2*(j - 1)*(j + 1)/4
Let s be (-9 - 3 - 15) + 29. Factor -1/5*j**s - 6/5*j + 7/5.
-(j - 1)*(j + 7)/5
Let x be -6 + (-261)/(-28)*(-36)/(-54). Let r(i) be the third derivative of 1/15*i**5 + 0 + i**2 - x*i**4 + 0*i + 4/21*i**3. Factor r(a).
4*(a - 1)*(7*a - 2)/7
Let f(t) = -6*t**3 + 4*t**2 + 10*t - 2. Let s(x) = -x**3 + x - 1. Let u = -109 - -107. Let k(y) = u*s(y) + f(y). Find n, given that k(n) = 0.
-1, 0, 2
Let y(n) be the third derivative of 0 + 9/70*n**7 - 1/20*n**6 + 0*n - 27/20*n**5 - 2*n**3 + 3*n**4 + 4*n**2. Factor y(r).
3*(r - 1)**2*(r + 2)*(9*r - 2)
Factor 407 - 22*b - 384 + 4*b**2 - 5*b**2.
-(b - 1)*(b + 23)
Let k(u) be the first derivative of -u**7/385 + u**6/66 - 2*u**5/55 + u**4/22 - u**3/33 - u**2 + 6. Let y(q) be the second derivative of k(q). Factor y(i).
-2*(i - 1)**3*(3*i - 1)/11
Let v(o) = -2*o**2 + 13*o. Let y be v(6). Suppose y*f - 96 = -66. Let -2/9*l**f - 2/3*l**4 + 2/3*l**2 - 2/9*l**3 + 4/9*l + 0 = 0. Calculate l.
-2, -1, 0, 1
Let b(p) be the first derivative of 15/16*p**2 + 1/8*p**3 + 3/2*p - 34. What is c in b(c) = 0?
-4, -1
Let t(x) be the second derivative of -x**4/42 - 64*x**3/21 - 1024*x**2/7 - 229*x. Factor t(v).
-2*(v + 32)**2/7
Let p(z) be the third derivative of z**6/300 - z**4/60 + 7*z**2 - 11*z. Find g such that p(g) = 0.
-1, 0, 1
Solve -30*z**2 + 15 - 15/2*z**3 + 5/2*z + 10*z**4 = 0 for z.
-1, 3/4, 2
Let w(o) be the first derivative of 2*o**3/3 + 23*o**2 - 216*o + 204. Factor w(f).
2*(f - 4)*(f + 27)
Let r be (-1)/(4 - 29/(-10)). Let n = 12/23 - r. Solve 0 - 2/3*f**2 + n*f = 0 for f.
0, 1
Let p(u) be the third derivative of 0 + 19/735*u**7 + 1/420*u**6 + 1/168*u**8 - 23/210*u**5 - 2/21*u**4 + 0*u - 3*u**2 + 4/21*u**3. What is z in p(z) = 0?
-2, -1, 2/7, 1
Let h(s) be the second derivative of 29 - s - 5/72*s**4 + 0*s**2 - 5/18*s**3. Solve h(t) = 0.
-2, 0
Let f(n) be the third derivative of -n**7/1050 + 7*n**6/600 - n**5/30 + 324*n**2. Determine q, given that f(q) = 0.
0, 2, 5
Let d be (-3)/(-6) - 5/(-2). Suppose 0 - 6 = -d*o. Find k, given that 3*k**2 - 36*k + 64 + k**2 + 0*k**o + 4*k = 0.
4
Let v be 296/32 + 10 + (-18 - 0). Factor 15/4*q**3 + 0*q - 5/2*q**2 - v*q**4 + 0.
-5*q**2*(q - 2)*(q - 1)/4
Let c be (-14 + (-170)/(-17))/(-6) - 38/(-33). Factor -34/11*g - 16/11 - 2/11*g**3 - c*g**2.
-2*(g + 1)**2*(g + 8)/11
Let m(o) be the first derivative of -o**7/70 + 3*o**6/20 - 4*o**4 + 17*o**2 + 12. Let d(g) be the second derivative of m(g). Determine a, given that d(a) = 0.
-2, 0, 4
Let w(f) = 4*f**5 + 10*f**4 + 4*f**3 + 6*f - 6. Let t(n) = -5*n**5 - 12*n**4 - 4*n**3 - 7*n + 7. Let j(z) = 6*t(z) + 7*w(z). Solve j(a) = 0.
-2, 0, 1
Let s = 1/8 + 13/24. Let f(d) be the first derivative of 0*d - 3 - s*d**3 + 3*d**2. Factor f(y).
-2*y*(y - 3)
Let g = -89 - -91. Let h be -5 + 23/g + -6. Factor -1/4*a + 3/8*a**4 + 0 - 1/8*a**2 + h*a**3.
a*(a + 1)**2*(3*a - 2)/8
Let q be -1*((-1 - -3) + -241). Suppose -235*o - 3 + 2*o**2 + q*o + 3 = 0. Calculate o.
-2, 0
Let m(x) = 46*x**3 + 76*x**2 - 34*x + 4. Let u(t) = t + 11. Let i be u(-6). Let c(k) = 45*k**3 + 75*k**2 - 33*k + 4. Let o(z) = i*m(z) - 4*c(z). Factor o(w).
2*(w + 2)*(5*w - 1)**2
Let t be (-42*(-7)/105)/((-9)/(-15)). Suppose -t*j**3 - 10/3*j**2 + 0 + 4/3*j = 0. Calculate j.
-1, 0, 2/7
Let t(b) be the second derivative of b**6/150 - b**5/100 + 31*b. Factor t(d).
d**3*(d - 1)/5
Suppose -1/4*s**2 - 4*s + 17/4 = 0. What is s?
-17, 1
Let f(c) be the second derivative of -c**4/21 - 22*c**3/21 - 60*c**2/7 + 2*c + 82. Factor f(i).
-4*(i + 5)*(i + 6)/7
Let x(g) be the first derivative of -1/12*g**2 + 1/24*g**4 - 13 + 0*g + 0*g**3. Find b such that x(b) = 0.
-1, 0, 1
Let h(d) be the third derivative of -d**5/600 + 11*d**4/240 - d**3/6 + d**2 - 5. Factor h(b).
-(b - 10)*(b - 1)/10
Let r(j) be the third derivative of j**5/360 + j**4/16 - 5*j**3/18 + j**2 + 25. Let r(s) = 0. What is s?
-10, 1
Let x(u) be the first derivative of -u**3 - 27*u**2/2 + 30*u