pose 31*j - 96 = 27*j. Determine h so that -9*h**3 + 4*h**3 + 96*h**2 + 69*h**3 + j*h + 12*h = 0.
-3/4, 0
Let d(k) = -2*k**4 - 8*k**3 + 8*k**2 - 7*k - 3. Let g(q) = 3*q**4 + 15*q**3 - 16*q**2 + 13*q + 5. Let a(p) = 5*d(p) + 3*g(p). What is r in a(r) = 0?
0, 1, 2
Let n be (-18)/(-48)*3*12/243. Let g(c) be the second derivative of -2*c + 0 - n*c**4 - 2/9*c**3 - 1/3*c**2. Factor g(u).
-2*(u + 1)**2/3
Let f(r) = -r**4 - r**3 + r - 1. Let v(m) = -2*m**4 - 8*m**3 - 14*m**2 + 44*m - 28. Let n(c) = 4*f(c) - v(c). Find j, given that n(j) = 0.
-3, 1, 2
Suppose 0*q**2 + 1/5*q**4 - 39/5*q**3 + 0*q + 0 = 0. Calculate q.
0, 39
Factor 0 - 3/5*s**3 - 3*s**2 + 18/5*s.
-3*s*(s - 1)*(s + 6)/5
Let c(w) be the second derivative of 3*w**6/2 - 47*w**5/4 + 365*w**4/12 - 205*w**3/6 + 15*w**2 + w + 9. Find r, given that c(r) = 0.
2/9, 1, 3
Let r(u) be the first derivative of -5/16*u**4 + 5/8*u**2 + 7 + 1/4*u**3 - 1/5*u**5 + 1/4*u. Let r(p) = 0. What is p?
-1, -1/4, 1
Let z(l) = 103*l**2 - l - 2. Let a be z(-1). Factor -99*j**5 + 3*j**2 + a*j**5 - 3*j**4 + 6*j - 9*j**3 + 0*j**4.
3*j*(j - 2)*(j - 1)*(j + 1)**2
Suppose 0 = -4*u - r + 7, 5*u + 52*r = 49*r. Determine z, given that -6/5*z**u + 3/5*z**2 + 3/5*z + 0 = 0.
-1/2, 0, 1
Let n(m) be the first derivative of 3*m**4/8 - 13*m**3/6 + 3*m**2 - 93. Suppose n(x) = 0. What is x?
0, 4/3, 3
Let o(q) = -4*q - 3. Let y be o(2). Let a = y - -35/3. Factor 0 + a*g + 1/3*g**3 + g**2.
g*(g + 1)*(g + 2)/3
Let f(v) be the first derivative of 5*v**6/6 + 18*v**5 + 75*v**4 + 280*v**3/3 + 416. Let f(x) = 0. What is x?
-14, -2, 0
Factor -14*b**3 - 22*b**3 + 15389 + 16*b**2 - 15389.
-4*b**2*(9*b - 4)
Factor -82/5 + 1/5*d**2 + 81/5*d.
(d - 1)*(d + 82)/5
Find u, given that -4 - 7*u + 4 - 4 - 5*u**2 + 2*u**2 = 0.
-4/3, -1
Let i(v) be the second derivative of v**4/12 + 7*v**3/18 + 2*v**2/3 + v + 1. Factor i(u).
(u + 1)*(3*u + 4)/3
Let f(g) = -g**3 - g**2 + 1. Let y(l) be the second derivative of 7*l**5/20 + 5*l**4/6 - l**3/2 - 5*l**2 - 7*l. Let m(c) = -4*f(c) - y(c). Factor m(q).
-3*(q - 1)*(q + 1)*(q + 2)
Factor -116/7*i**2 + 8/7 - 108/7*i.
-4*(i + 1)*(29*i - 2)/7
Let q(n) = 2*n**3 - n**2 + n + 1. Let z(x) = 2*x**4 + 38*x**3 + 30*x**2 + 26*x + 8. Let k(a) = -8*q(a) + z(a). Solve k(o) = 0.
-9, -1, 0
Let u be (4 - 4)/(-2) + 2. Let y be (-10)/(-4 + 0 + u). Solve -d - 6*d**2 - 5*d - 4 + 2*d + y*d**2 = 0 for d.
-2
Let h be (2/2*-1)/((-7)/(-273)). Let u be h/9 + 4 - -1. Let -2/3*c**2 + 2/3*c - 2/3*c**3 + u = 0. Calculate c.
-1, 1
Let x = 8626 + -8624. Factor -2/5*c**4 + 0 - 4/5*c**x - 6/5*c**3 + 0*c.
-2*c**2*(c + 1)*(c + 2)/5
Let v be -1 + 5/(-2 + 5 - 2). Solve -4 - 24*f - 9 + 49 - 104*f**2 + 36*f**v - 8*f**5 = 0.
-1, 1/2, 3
Suppose -63*m = -76*m. Let q(y) be the second derivative of -1/24*y**6 + m - 1/40*y**5 - 4*y + 2/3*y**3 + 1/2*y**2 + 5/16*y**4. Find f, given that q(f) = 0.
-1, -2/5, 2
Let p(n) be the second derivative of -2/21*n**7 + 0 - 2/5*n**6 + 0*n**3 - 1/3*n**4 + 0*n**2 - 6*n - 3/5*n**5. Factor p(v).
-4*v**2*(v + 1)**3
Let a(y) be the second derivative of -y**7/105 - y**6/30 + y**5/30 + y**4/6 + 7*y**2/2 - 7*y. Let n(h) be the first derivative of a(h). Factor n(o).
-2*o*(o - 1)*(o + 1)*(o + 2)
Suppose 3*r + 141 = 12*l - 15*l, -3*r = 2*l + 90. Let v = l - -54. Determine f so that -6/5*f**4 - 2/5*f**2 + 0*f + 2/5*f**5 + 0 + 6/5*f**v = 0.
0, 1
Let s(n) = 18*n**2 + 24*n + 144. Let f(p) = -2*p**2 - 3*p - 18. Let b(y) = 33*f(y) + 4*s(y). Factor b(o).
3*(o - 2)*(2*o + 3)
Let h = 0 - -17. Suppose -4*z + m = -0*m - h, z - 18 = 3*m. Factor -8*r**3 + z*r**3 + 8*r**3.
3*r**3
Let c(x) be the second derivative of -x**5/20 - 2*x**4/3 + 7*x**3/6 - 6*x**2 + 3*x. Let g be c(-9). Solve 2*l**2 - g*l + 20 + 6*l - 20*l + 3*l**2 = 0.
2
Let s = 764433/286 + -29026/11. Let r = -67/2 + s. Suppose 18/13*n**3 + 40/13*n**2 + 0 + r*n = 0. What is n?
-2, -2/9, 0
Let b = -991/6 - -331/2. Solve 0*j**3 + b*j**2 - 1/3*j**4 + 0*j + 0 = 0 for j.
-1, 0, 1
Suppose -5*l - 2*o + 19 = -6*o, 7 = l - 4*o. Let a(r) be the first derivative of -4/13*r + 3/26*r**4 + 9 + 8/39*r**l - 1/13*r**2. Factor a(x).
2*(x + 1)**2*(3*x - 2)/13
Let n = 34 - 4. Let g(r) = r + 1. Let i(b) = -b**3 - b**2 - 5*b - 5. Let u(p) = n*g(p) + 5*i(p). Factor u(q).
-5*(q - 1)*(q + 1)**2
Let k(c) be the third derivative of 0*c + 1/42*c**7 - 5/3*c**3 - 1/4*c**5 + 23*c**2 + 0 - 1/24*c**6 + 25/24*c**4. Factor k(v).
5*(v - 1)**3*(v + 2)
Let w = 17 + -116/7. Suppose 3/7*c**2 - 3/7*c**3 + w*c - 3/7*c**4 + 0 = 0. What is c?
-1, 0, 1
Let c(n) be the third derivative of -1/450*n**5 + 0 + 1/36*n**4 + 0*n - 4/45*n**3 - 11*n**2. Factor c(k).
-2*(k - 4)*(k - 1)/15
Let x be (0 - 1) + (12 - 0). Let r be (x/(-22))/(1/(-12)). Find a, given that 24*a**2 - r*a**4 - 3*a**3 + 15*a**3 + 0*a**5 - 3*a**5 = 0.
-2, 0, 2
Let c(o) be the third derivative of -1/8*o**4 - 1/60*o**5 + 1/40*o**6 + 0 + 1/6*o**3 + 4*o**2 + 0*o. Solve c(j) = 0 for j.
-1, 1/3, 1
Let p(a) be the first derivative of -a**4/14 + 8*a**3/21 - 4*a**2/7 + 194. Factor p(l).
-2*l*(l - 2)**2/7
Let c(t) be the second derivative of t**4/96 - 7*t**3/4 + 441*t**2/4 + 38*t + 2. Factor c(n).
(n - 42)**2/8
Let d(r) be the first derivative of -r**4 + 5*r**2 + 11 - 7*r + 5*r**2 - 4*r**2 - r. Factor d(p).
-4*(p - 1)**2*(p + 2)
Let u(p) be the first derivative of -8*p**3/21 + 5*p**2/7 + 6*p - 74. Find b, given that u(b) = 0.
-7/4, 3
Let c(l) = 3*l**3 + l**2 - 16*l. Let p(m) = -m**3 + m**2 + 2*m + 1. Suppose -13*u + 7 = -20*u. Let x(i) = u*c(i) - 4*p(i). Suppose x(t) = 0. Calculate t.
1, 2
Let p(f) be the second derivative of -f**4/96 - f**3/12 - f**2/4 - 91*f. Factor p(g).
-(g + 2)**2/8
Let n = -1 + 3. Let w(h) = h**2 - 8*h + 1. Let b be w(9). Factor 2*y**n - b*y - 2*y + 4 + 6*y.
2*(y - 2)*(y - 1)
Let i(g) be the first derivative of -3*g**4/4 + g**3 + 62. Suppose i(b) = 0. What is b?
0, 1
Let t(z) = -z - 8. Let b be t(-11). Suppose -l**5 + 4*l**2 - 2*l**3 - 4*l**b + l**5 + 2*l**5 = 0. What is l?
-2, 0, 1
Let f(q) be the second derivative of -216/7*q**2 + q + 0 - 36/7*q**3 - 3/7*q**4 - 1/70*q**5. Factor f(z).
-2*(z + 6)**3/7
Let y(s) be the first derivative of -10/3*s**3 - 5/6*s**6 - 25/4*s**4 - 4*s**5 - 9 + 0*s**2 + 0*s. Suppose y(u) = 0. What is u?
-2, -1, 0
Suppose 0 = 5*k - 0*k - 25. Suppose -4*i = -7 - k. Suppose 15*o - 3*o + 11 + 0 - i + 4*o**2 = 0. What is o?
-2, -1
Let f(l) = -4*l**4 - 5*l**3 + 25*l**2 + 5*l - 26. Let b(o) = -4*o**4 - 4*o**3 + 24*o**2 + 4*o - 24. Let k(a) = -5*b(a) + 4*f(a). Let k(n) = 0. What is n?
-2, -1, 1, 2
Suppose 4*f - 12 = 4*k - 36, -3*k + 10 = -f. Solve 4*j**k + 3*j**3 + 56*j**4 + 2 - 5*j**2 - 3*j - 57*j**4 = 0 for j.
-1, 1, 2
Let n be -1 - (276/1540)/((-10)/(-25)). Let w = 4/77 - n. Factor 3/8*m**2 + 3/2 + w*m.
3*(m + 2)**2/8
Let c(l) be the first derivative of l**8/3360 + l**7/840 - l**6/180 - l**5/30 + 8*l**3 + 15. Let x(o) be the third derivative of c(o). Factor x(y).
y*(y - 2)*(y + 2)**2/2
Factor 12/7*k - 16/7 - 2/7*k**2.
-2*(k - 4)*(k - 2)/7
Let w = -661 - -6611/10. Let k(d) be the first derivative of 1/5*d**2 + 2 - w*d**4 + 1/25*d**5 + 0*d**3 - 1/5*d. Factor k(h).
(h - 1)**3*(h + 1)/5
Let v(l) be the third derivative of -1875/8*l**4 + 325/6*l**5 - 5/336*l**8 - 21*l**2 + 0 + 1/2*l**7 + 3125/6*l**3 - 85/12*l**6 + 0*l. Let v(d) = 0. Calculate d.
1, 5
Find l, given that -2/17*l**2 - 88/17*l - 968/17 = 0.
-22
Let u(v) be the second derivative of 9*v + 0*v**2 + 3/5*v**5 + 0*v**3 - 3/4*v**4 - 1/10*v**6 - 2. Determine i, given that u(i) = 0.
0, 1, 3
Let o = 135 + -267/2. Let g(j) be the first derivative of -2*j**3 + 3/4*j**4 + o*j**2 + 0*j + 2. Determine x, given that g(x) = 0.
0, 1
Factor -46*y**4 + 11*y**3 - 12*y + y**3 + 96*y**4 - 2*y**2 - 48*y**4.
2*y*(y - 1)*(y + 1)*(y + 6)
Let x = -90 + 140. Let p = x - 45. Determine d, given that -d**4 + 0*d - 7/2*d**3 + 0 + 7/2*d**p + d**2 = 0.
-1, 0, 2/7, 1
Let z(p) = -63*p + 1452. Let j be z(23). Determine i, given that 0 - 2/3*i + i**j + 1/3*i**2 = 0.
-1, 0, 2/3
Let a(j) be the second derivative of j**7/42 - 4*j**6/15 - 3*j**5/20 + 11*j**4/6 + 8*j**3/3 - 8*j. Factor a(z).
z*(z - 8)*(z - 2)*(z + 1)**2
Let t be (-5)/(-15)*21 + -4. Solve d**2 - 19*d**2 - 8*d + d**3 - 14*d**2 - 27*d**t - 6*d**4 = 0.
-2, -1/3, 0
Let c = 16 + 54. Suppose 4*o - 90 = -c. What is b in 46/9*b**3 + 14/9*b**2 + 2/9 - 32/9*b**o - 16/9*b*