 + 16. Let x be (-3 + 49/c)*3. Suppose 2/5 - 6/5*t**2 - x*t**4 - 2/5*t + 2*t**3 = 0. Calculate t.
-1/2, 1
Let m(l) be the third derivative of -1/480*l**6 + 0*l**3 + 0*l**4 + 0 + 1/120*l**5 + 4*l**2 + 0*l - 1/840*l**7. Suppose m(w) = 0. Calculate w.
-2, 0, 1
Let j(w) be the third derivative of w**9/272160 + w**8/45360 + w**7/22680 - w**5/20 + w**2. Let l(t) be the third derivative of j(t). What is z in l(z) = 0?
-1, 0
Let c be 4/(2/(-5) - 0). Let w = 17 + c. What is h in h - 2 - w*h - 2*h**4 - 12*h**2 - 2*h - 8*h**3 = 0?
-1
Let w(j) = -5*j**2 + 8*j + 1. Let r(n) = 6*n**2 - 9*n - 1. Let c(l) = l**2 + 4*l + 2. Let k be c(-5). Let o(s) = k*w(s) + 6*r(s). Let o(g) = 0. Calculate g.
-1
Suppose u + u = 4*n + 40, -n - u - 10 = 0. Let p = n + 10. Factor p + 2/11*j**3 - 2/11*j**2 + 0*j.
2*j**2*(j - 1)/11
Let b(w) = -3*w**2 + 10*w + 19 + w**2 + 3*w**2 - 7. Let a be b(-9). Factor -a + 2*o**2 - 1 + 4 - 2.
2*(o - 1)*(o + 1)
Let k(r) be the third derivative of 0 + 0*r**3 + 1/18*r**4 - 1/45*r**5 + r**2 + 1/360*r**6 + 0*r. Factor k(b).
b*(b - 2)**2/3
Let h(s) = -s**4 + s**2 - 1. Let t(p) = -2*p + 2*p**2 - 6*p**3 - 3*p**3 + 10*p**4 + 0*p**3 + 0 + 5 - p**5. Let u(i) = -15*h(i) - 3*t(i). Factor u(k).
3*k*(k - 2)*(k - 1)**3
Let x = 11 + -6. Let 3*z**2 - 2*z - 3 + 3 + x*z**3 = 0. What is z?
-1, 0, 2/5
Let f(g) be the first derivative of g**6/18 - 14*g**5/45 + 5*g**4/9 - 8*g**3/27 + 22. Factor f(t).
t**2*(t - 2)**2*(3*t - 2)/9
Let d = -27 - -60. Factor -14*i - 10*i**3 + 4 + 0*i**4 + 2*i**4 - d*i**2 + 51*i**2.
2*(i - 2)*(i - 1)**3
Let 8/5*n - 6/5*n**2 + 8/5 = 0. Calculate n.
-2/3, 2
Let k(q) = 60*q + 542. Let p be k(-9). Find a, given that 0 - 2/7*a**4 - 4/7*a**3 + 2/7*a**p + 4/7*a = 0.
-2, -1, 0, 1
Factor -1/2*x**3 + x**2 - 1 + 1/2*x.
-(x - 2)*(x - 1)*(x + 1)/2
Let k be 8/24*3/(-70)*-1. Let u(m) be the second derivative of -2/7*m**2 - 3*m - 1/7*m**3 + 0 + k*m**5 + 0*m**4. Factor u(a).
2*(a - 2)*(a + 1)**2/7
Let l be (0 + 0)/(4/(-4)). Let c = 2 - l. Find t such that -c*t**3 + 2*t**4 - t**4 + 3*t**3 = 0.
-1, 0
Let k(x) be the second derivative of 0 + 1/30*x**4 + 0*x**2 + 1/15*x**3 - 2*x - 1/50*x**5 - 1/75*x**6. Determine g, given that k(g) = 0.
-1, 0, 1
Let x be (130/105)/2 - (-2)/(-6). Factor 4/7 - 4/7*r**2 + x*r - 2/7*r**3.
-2*(r - 1)*(r + 1)*(r + 2)/7
Let d be 1/((-20)/(-32))*25. Let v be d/110 - (1 - 1). Suppose 2/11*y**4 - 4/11*y + 0*y**2 + v*y**3 - 2/11 = 0. What is y?
-1, 1
Suppose -4*k + 12 = j, 4*j - 9 = 4*k - 41. Suppose 5*u + 3*u + 16*u**2 + 16*u - 4*u + k = 0. What is u?
-1, -1/4
Factor 2/11*f**2 + 0*f - 8/11.
2*(f - 2)*(f + 2)/11
Suppose 3*j - 12*j - 3*j**4 + 6 + 9*j**3 - 15*j**2 + 12*j**2 = 0. What is j?
-1, 1, 2
Let g be 8/(-10)*35/504*-4. Suppose 2/9 + g*c**2 - 4/9*c = 0. Calculate c.
1
Let a(y) = y**2 - y - 2. Let g be a(3). Let o(t) be the first derivative of -1/18*t**g - 2/27*t**3 + 2 + 2/9*t + 1/9*t**2. Determine f, given that o(f) = 0.
-1, 1
Suppose -5*m + 4*m + 6*m = 0. Let b(p) be the second derivative of -3/40*p**5 - 1/12*p**6 + 1/24*p**4 + 1/12*p**3 - p + 0 - 1/42*p**7 + m*p**2. Factor b(o).
-o*(o + 1)**3*(2*o - 1)/2
Let v(d) be the second derivative of d**6/20 + d**5/4 + d**4/8 - d**3 - 5*d**2/2 - 4*d. Let g(o) be the first derivative of v(o). Factor g(k).
3*(k + 1)*(k + 2)*(2*k - 1)
Determine z so that -5*z - 13*z**2 - 4*z**3 - 10*z + z**2 - 4 + 3*z = 0.
-1
Let n = -2 - -5/2. Factor 3/2*x + 0 - n*x**2.
-x*(x - 3)/2
Suppose -376*n = -366*n. What is u in -1/4*u**2 + 0 + n*u = 0?
0
Let c(v) = -3*v - 43. Let s be c(-15). Factor -6/11*f - 4/11*f**s - 2/11.
-2*(f + 1)*(2*f + 1)/11
Let y(t) be the first derivative of -4*t**3/15 - 2*t**2/5 + 8*t/5 + 1. Find n, given that y(n) = 0.
-2, 1
Suppose -70/3*i**3 - 16/15 - 76/3*i**2 - 136/15*i = 0. What is i?
-2/5, -2/7
Let g be (-10)/(-4)*(-102)/(-85). Factor 0 - 4/9*y + 2/9*y**g - 2/9*y**2.
2*y*(y - 2)*(y + 1)/9
Let h(x) be the second derivative of -5*x**4/12 + 10*x**3/3 - 15*x**2/2 - 12*x. Find s such that h(s) = 0.
1, 3
Let l(k) = -k + 1. Let c(j) = j**2 - j. Let q(a) = -2*a**2 + 2*a - 1. Let p(h) = 7*c(h) + 4*q(h). Let z(u) = 6*l(u) + 2*p(u). Factor z(t).
-2*(t + 1)**2
Let z(d) be the third derivative of 0*d**3 - 1/672*d**8 - 1/240*d**6 - 3*d**2 + 0*d**4 + 0 + 0*d - 1/210*d**7 + 0*d**5. Factor z(m).
-m**3*(m + 1)**2/2
Let l(w) = w**3 + w**2 + 3. Let m be l(0). Let -3*a**3 - 5 - 3*a - 9*a**2 - 1 - 6*a + m = 0. What is a?
-1
Suppose -9 + 3 = 3*b. Let y = 5 + b. What is a in 0 + 5/3*a**5 - 2/3*a**2 + 0*a + 1/3*a**y + 8/3*a**4 = 0?
-1, 0, 2/5
Let c(n) be the first derivative of -n**5/5 - n**4/4 + n**3/6 - 3*n + 4. Let v(m) be the first derivative of c(m). Let v(i) = 0. Calculate i.
-1, 0, 1/4
Let v(q) be the second derivative of 7*q**4/6 - 44*q**3/3 + 12*q**2 - 2*q + 1. What is t in v(t) = 0?
2/7, 6
Let x(m) be the first derivative of -m**4 + 6*m**2 - 8*m + 5. Find i such that x(i) = 0.
-2, 1
Let y be ((-278)/9)/((-8)/12). Let c = y - 46. Factor c*x**2 - 1/3 - 1/3*x**3 + 1/3*x.
-(x - 1)**2*(x + 1)/3
Let g = 42 - 106/3. Let m be (-1)/(-1 + 3 + (-5)/2). What is o in -6*o**m + g*o + 7/3*o**3 - 8/3 - 1/3*o**4 = 0?
1, 2
Let p = 637/5 - 127. Factor -4/5 - 6/5*h - p*h**2.
-2*(h + 1)*(h + 2)/5
Let c be (-2)/(-7) + (-63)/392. Let u(v) be the first derivative of -c*v**2 + 1/16*v**4 + 1/20*v**5 - 1 - 1/4*v**3 + 1/2*v. Factor u(a).
(a - 1)**2*(a + 1)*(a + 2)/4
Let z(a) be the first derivative of -3*a**5/5 - 3*a**4 - 6*a**3 - 6*a**2 - 3*a + 4. Factor z(x).
-3*(x + 1)**4
Let a = -5 + 10. Let 7/5*l**4 - 8/5*l**2 - 2/5*l**3 + 1/5 - 2/5*l + 4/5*l**a = 0. Calculate l.
-1, 1/4, 1
Suppose 70 = 5*w + 40. Let y(n) be the second derivative of -2/3*n**3 + 1/5*n**5 - 1/15*n**w + 0 + n + 0*n**4 + n**2. Let y(s) = 0. Calculate s.
-1, 1
Let w(z) be the third derivative of 0*z + 0*z**5 + 0 - 1/80*z**6 + 0*z**4 + 0*z**3 - 3*z**2. Factor w(x).
-3*x**3/2
Let o(z) = -z**2 - 6*z + 3. Let q be o(-5). Suppose 2*h + y - q = 2*y, h + 6 = -2*y. Let 7 + 5*u**3 - 5 - h*u - 8*u**2 + 3*u = 0. Calculate u.
-2/5, 1
Let n(x) = -29*x**4 + 25*x**3 + 11*x**2 + 13*x + 13. Let h(q) = -14*q**4 + 12*q**3 + 5*q**2 + 6*q + 6. Let v(y) = -13*h(y) + 6*n(y). Factor v(o).
o**2*(2*o - 1)*(4*o - 1)
Let m(w) be the first derivative of w**5/5 - w**3/3 + w**2 + 2*w - 3. Let l(q) = -3*q**4 + 3*q**2 - 7*q - 7. Let s(y) = -2*l(y) - 7*m(y). Factor s(c).
-c**2*(c - 1)*(c + 1)
Let 2/3*a**3 + 2/3*a - 4/3*a**2 + 0 = 0. Calculate a.
0, 1
Let m(a) be the first derivative of -2*a**5/5 - 3*a**4/2 + 8*a**3/3 + 12. Factor m(q).
-2*q**2*(q - 1)*(q + 4)
Factor 8*m + 25*m**4 + 20*m**2 + 12*m**3 - 21*m**4 + 4*m**3.
4*m*(m + 1)**2*(m + 2)
Let x(a) = -11*a**2 + 9*a - 16. Let k(s) = -100*s**2 + 80*s - 145. Let l(w) = 6*k(w) - 55*x(w). Suppose l(d) = 0. Calculate d.
1, 2
Solve -8*s**2 + 2/3*s**3 + 0*s + 0 = 0 for s.
0, 12
Let a(o) be the first derivative of -o**6/240 - o**5/60 - o**4/48 + o**2/2 - 2. Let v(z) be the second derivative of a(z). Factor v(g).
-g*(g + 1)**2/2
Suppose -2*u + 12 = -0*u. Let w = 8 - u. Factor w*q - 7*q**2 + 2*q**2 + 9*q**2.
2*q*(2*q + 1)
Suppose 0 = -x + 3 + 1. Suppose 0 = x*c - 16, -5*c + 5 = 2*p - 23. Solve -2/9*q**p + 0*q**3 + 0 + 0*q + 2/9*q**2 = 0.
-1, 0, 1
Let k(u) be the second derivative of u**5/80 - u**3/8 + u**2/4 + 17*u. Find y, given that k(y) = 0.
-2, 1
Let o(s) be the first derivative of 2/27*s**3 + 2/9*s + 2/9*s**2 - 5. Factor o(l).
2*(l + 1)**2/9
Let p(l) be the third derivative of 1/60*l**6 - 1/70*l**7 + 0 + l**2 + 0*l + 1/336*l**8 - 1/8*l**4 + 1/6*l**3 + 1/30*l**5. Solve p(a) = 0 for a.
-1, 1
Let q(h) be the second derivative of -h**8/1008 - h**7/840 + h**6/540 + h**3/3 - 4*h. Let d(x) be the second derivative of q(x). Factor d(t).
-t**2*(t + 1)*(5*t - 2)/3
Let v(a) be the second derivative of -a**5/12 - a**4/6 + a**3/2 + a**2/3 + 15*a. Factor v(t).
-(t - 1)*(t + 2)*(5*t + 1)/3
Let z(k) be the second derivative of -k**7/168 - 7*k**6/120 + 9*k**5/40 - k**4/24 - 17*k**3/24 + 9*k**2/8 + 15*k. Factor z(h).
-(h - 1)**3*(h + 1)*(h + 9)/4
Let j be ((-64)/10)/((-62)/8). Let k = j + 24/31. Factor k + 2/5*h**2 + 8/5*h.
2*(h + 2)**2/5
Let t(x) = -7*x**2 - 5*x + 2. Let w = -17 + 39. Let b(f) = -26*f + 0*f**2 + 0*f**2 + 10 - 8*f**2 - 28*f**2. Let o(c) = w*t(c) - 4*b(c). Solve o(a) = 0.
-1, 2/5
Solve -2/7*v**3 - 2/7*v**2 + 0 + 0*v = 0.
-1, 0
Let g(r) = -r*