0*y**2. Let q(h) = 0. Calculate h.
1
Let l(q) be the second derivative of -3*q**5/20 + q**4/2 + 4*q. Suppose l(k) = 0. Calculate k.
0, 2
Let v(c) = -c**3 - c**2 + 3*c + 1. Let s be v(-4). Factor 3*y**4 - y**2 + y**5 + 40*y**3 - 6*y**4 - s*y**3.
y**2*(y - 1)**3
Let r(v) = 4*v**2 - 26*v + 22. Let g(p) = -p + 1. Let x(c) = 6*g(c) - r(c). Factor x(y).
-4*(y - 4)*(y - 1)
Suppose -9*n = -13*n. Determine u so that n*u**3 + 0*u - 2/7 + 4/7*u**2 - 2/7*u**4 = 0.
-1, 1
Let a(s) = s**2 - s. Let d(g) = -2*g**3 + 6*g**2 - 4*g. Let r(y) = 7*y**3 + 2*y**2 - 1. Let w be r(1). Let j(t) = w*a(t) - d(t). Factor j(c).
2*c*(c - 1)*(c + 2)
Let j(a) be the second derivative of -a**6/45 + a**5/12 - a**4/12 - a**3/18 + a**2/6 + 8*a. Solve j(u) = 0.
-1/2, 1
Let w(b) be the third derivative of b**5/30 + b**4/12 + 14*b**2. What is l in w(l) = 0?
-1, 0
Let z(t) be the third derivative of -2*t**7/315 + t**6/45 + 4*t**5/45 - 4*t**4/9 + 30*t**2. Factor z(m).
-4*m*(m - 2)**2*(m + 2)/3
Let r(f) be the third derivative of f**6/200 - 3*f**5/50 + 3*f**4/10 - 4*f**3/5 + 8*f**2. Solve r(w) = 0 for w.
2
Let z be 1/2 + 3 + 90/(-28). Factor -2/7*p**3 + 0 - z*p - 4/7*p**2.
-2*p*(p + 1)**2/7
Let d(u) be the first derivative of 0*u**2 + 3 - 2/21*u**3 + 2/7*u. Factor d(j).
-2*(j - 1)*(j + 1)/7
Let j = -785 - -11759/15. Let q = -2/5 - j. Factor -2/9*i - q*i**2 + 0.
-2*i*(3*i + 1)/9
Let v = -11 - -23. Suppose -7*x + 10*x - v = 0. Suppose -12/7*w**2 - 4/7 + 2*w - 2/7*w**3 + 4/7*w**x = 0. Calculate w.
-2, 1/2, 1
Let k(b) be the third derivative of b**8/84 - 2*b**7/35 + 53*b**6/480 - 53*b**5/480 + b**4/16 - b**3/48 - 2*b**2. Suppose k(c) = 0. What is c?
1/4, 1/2, 1
Let h(b) be the third derivative of b**7/3780 - b**6/540 - b**4/8 - b**2. Let t(d) be the second derivative of h(d). Let t(c) = 0. What is c?
0, 2
Let f(a) be the third derivative of -a**10/151200 + a**9/60480 - a**5/15 + 3*a**2. Let d(k) be the third derivative of f(k). Factor d(l).
-l**3*(l - 1)
Let d be 1 + -3 - 0/3. Let p be d + 2 - (0 - 2). Factor -1/2*b**5 + 0 + b**4 - 1/2*b**3 + 0*b + 0*b**p.
-b**3*(b - 1)**2/2
Let h = 17 + -10. Let d(j) be the third derivative of -3*j**2 + 0*j - 1/60*j**6 + 1/12*j**4 + 0*j**3 + 1/30*j**5 + 0 - 1/105*j**h. What is i in d(i) = 0?
-1, 0, 1
Let s(w) be the second derivative of -w**6/105 + w**4/21 - w**2/7 - 6*w. Factor s(b).
-2*(b - 1)**2*(b + 1)**2/7
Factor -c**2 - 3/2*c**3 + 0 - 1/6*c.
-c*(3*c + 1)**2/6
Determine f so that 24/5*f**2 - 134/5*f**4 - 126/5*f**5 - 16/5*f + 0 + 252/5*f**3 = 0.
-2, -2/7, 0, 2/9, 1
Let k = -136/3 + 46. Factor k*w**2 + 2/3*w**3 - 2/3*w**4 + 0 - 2/3*w.
-2*w*(w - 1)**2*(w + 1)/3
Let x = -3 - -6. Let n(u) be the second derivative of 5/18*u**4 + 5/18*u**x + 1/6*u**2 + 0 + 1/6*u**5 + 2*u + 1/18*u**6 + 1/126*u**7. Solve n(b) = 0.
-1
Let o(j) be the third derivative of 1/336*j**8 + 1/210*j**7 + 1/6*j**3 - 1/60*j**6 + 0 + 4*j**2 - 1/30*j**5 + 1/24*j**4 + 0*j. Determine u, given that o(u) = 0.
-1, 1
Let i(r) be the first derivative of r**5/30 - r**4/6 + r**2/2 + 1. Let u(x) be the second derivative of i(x). Solve u(d) = 0.
0, 2
Suppose 4*y = 5*j + 7, y - j = -13 + 15. Find i such that 0*i + 6/13*i**4 - 4/13*i**2 + 0 - 2/13*i**y = 0.
-2/3, 0, 1
Let q = -133/2 - -79. Find w such that 10*w**2 + 0 + q*w**3 + 2*w = 0.
-2/5, 0
Factor 14/3*l + 8 + 2/3*l**2.
2*(l + 3)*(l + 4)/3
Factor 0*n**4 - 13*n**2 + 0*n - 6*n**3 - 4 - n**4 - 4*n - 8*n.
-(n + 1)**2*(n + 2)**2
Let p(b) be the first derivative of 6*b**5/5 + 2*b**4 + b**3/3 + 2*b - 2. Let d(v) = -17*v**4 - 25*v**3 - 3*v**2 - 7. Let s(o) = 4*d(o) + 14*p(o). Factor s(m).
2*m**2*(2*m + 1)*(4*m + 1)
Let x(i) be the second derivative of i**5/5 + i**4/3 + 3*i. Factor x(j).
4*j**2*(j + 1)
Let t(o) = -1. Let f(i) = 2*i**2 - 10*i + 4. Let m(h) = -f(h) + 4*t(h). Solve m(p) = 0.
1, 4
Let p be (12/(-15))/(6/(-5)). Suppose 0 = -n + 4*n + a - 7, -2*n - 2*a = 2. What is x in -1/3*x**5 - p*x**2 + x**n + x - 1/3 - 2/3*x**3 = 0?
-1, 1
Determine f so that -9*f - 7*f**2 - 5*f**2 - 4*f**3 + f = 0.
-2, -1, 0
Let r = 0 - 0. Let s = 3 + r. Factor 0 - 2/7*p - 8/7*p**2 - 12/7*p**s - 2/7*p**5 - 8/7*p**4.
-2*p*(p + 1)**4/7
Let v = 758/9 + -84. Let f(d) be the first derivative of 2/3*d**2 - v*d**3 - 3 + 0*d. Solve f(m) = 0.
0, 2
Factor -9*m + 29*m**3 + m**5 - 47*m**3 + 6 + 32*m**2 + 2*m**4 - 14*m.
(m - 1)**4*(m + 6)
Let z = 3 - 0. Suppose z = -k + 6. Factor -2/3 - 4*u**2 - 8/3*u**k - 8/3*u - 2/3*u**4.
-2*(u + 1)**4/3
Let u be -10 + 8 + 48/20. Find n, given that 0 + 2/5*n**2 - u*n = 0.
0, 1
Let r be -1 + 1 + 24/18. Factor -r - 1/3*w**2 + 4/3*w.
-(w - 2)**2/3
Suppose 39 - 34 = 2*z + w, -2*w - 6 = 0. Determine g, given that 0*g**z - g**3 + 1/2*g**5 + 1/2*g + 0 + 0*g**2 = 0.
-1, 0, 1
Suppose 3*f = 3*j - 18, 0*f - 6 = -5*j - 3*f. Suppose 8 = j*t - t. Determine l, given that l**t + 0*l - l**3 + 0*l - 2*l**4 = 0.
-1, 0
Suppose -3*d + 1 = -8. Suppose -3*s**3 - 8*s**2 - s + 5*s**3 - d*s + 2*s**3 + 8 = 0. Calculate s.
-1, 1, 2
Let u(d) be the first derivative of -d**6/3 - 16*d**5/15 - 11*d**4/9 - 16*d**3/27 - d**2/9 - 19. Factor u(l).
-2*l*(l + 1)**2*(3*l + 1)**2/9
Suppose 0 = 2*z + 2*z - k - 22, z - 5*k = 15. Let g be (-4)/(-16 - (z - 3)). Factor 2/9*m**4 + 2/9*m**5 - g*m**2 - 2/9*m**3 + 0 + 0*m.
2*m**2*(m - 1)*(m + 1)**2/9
Let i(h) be the second derivative of -7*h**4/12 - 5*h**3/3 + 2*h**2 + 3*h. Let t(r) = -57*r**2 - 81*r + 33. Let g(j) = 33*i(j) - 4*t(j). What is f in g(f) = 0?
-2, 0
Let m = -1/239 - -3827/717. Find b such that 104/3*b + 50*b**3 - 220/3*b**2 - m = 0.
2/5, 2/3
Let m be 2*(4 + 4 + -4). Let h(d) = 11*d**3 - 8*d**2 - 17*d + 2. Let b(l) = 4*l**3 - 3*l**2 - 6*l + 1. Let g(o) = m*b(o) - 3*h(o). Suppose g(q) = 0. What is q?
-1, 2
Let u(z) be the first derivative of z**8/5880 - z**6/1260 - 2*z**3/3 - 2. Let q(o) be the third derivative of u(o). Let q(y) = 0. Calculate y.
-1, 0, 1
Let h(r) be the second derivative of 0*r**3 + 0*r**2 + 1/60*r**4 + 0 + 1/150*r**6 + 1/50*r**5 + 4*r. Determine g so that h(g) = 0.
-1, 0
Let i be 10/4*17/85. Factor i*v**2 + 1/2*v**3 - 1/2 - 1/2*v.
(v - 1)*(v + 1)**2/2
Factor 13/2*x**2 + 1/2 - 6*x**3 + 2*x**4 - 3*x.
(x - 1)**2*(2*x - 1)**2/2
Factor 1/3*o**3 - 2/3*o**2 + 0 + 0*o.
o**2*(o - 2)/3
Let s be 2/((-1 + 3)/2). Let -2*l**4 + l**s + 2*l**3 - 2*l**4 - 2*l**2 + 3*l**2 = 0. What is l?
-1/2, 0, 1
Let r(p) be the first derivative of -p**8/560 - 3*p**7/350 - p**6/100 - 7*p**2/2 - 3. Let s(f) be the second derivative of r(f). What is q in s(q) = 0?
-2, -1, 0
Let c = 4 - 11/3. Let f(d) be the first derivative of -c*d**2 + 4 + 1/3*d + 1/9*d**3. Suppose f(m) = 0. Calculate m.
1
Let x be (-1 - 1)/((-25)/25). Determine s so that 0 + 4/5*s - 2/5*s**x = 0.
0, 2
Factor 0*a - 2/7*a**3 + 0 - 4/7*a**2.
-2*a**2*(a + 2)/7
Factor 26/7*h**2 + 8/7*h + 10/7*h**3 - 8/7.
2*(h + 1)*(h + 2)*(5*h - 2)/7
Let a = 16 + -14. Factor 3*w**5 + 2*w + 0*w**5 - w**5 + 10*w**4 + 8*w**a + 12*w**3 - 2*w**4.
2*w*(w + 1)**4
Let n(d) be the first derivative of -3 + 7/6*d**3 - 3*d**2 - 2*d. Factor n(j).
(j - 2)*(7*j + 2)/2
Let u be -2 + 3 - (-2)/4. Suppose 0 = 4*g - 3*g - 3. Solve 1/2*n + 0 - u*n**g - n**2 = 0 for n.
-1, 0, 1/3
Suppose 21*m**4 - 5*m**2 - 4*m**3 + 2*m**2 - 12*m**5 - 2*m**3 = 0. What is m?
-1/4, 0, 1
Let b(i) be the first derivative of -i**4/20 + i**3/10 - 5*i - 2. Let q(t) be the first derivative of b(t). Factor q(c).
-3*c*(c - 1)/5
Let o(p) be the second derivative of p**6/30 - p**5/20 - p**4/12 + p**3/6 - 2*p. Determine x so that o(x) = 0.
-1, 0, 1
Let y be (-1)/2 + (-20)/(-8). Factor -x**2 + y*x**2 - 4*x + 6*x.
x*(x + 2)
Let p(b) be the second derivative of -b**4/4 + 2*b**3 + 23*b. Factor p(f).
-3*f*(f - 4)
Let x be 9/(-30)*-2 - -1. Let l(z) be the second derivative of 4/5*z**3 - 1/5*z**4 + 1/50*z**5 + 0 - x*z**2 - z. What is t in l(t) = 0?
2
Let t(u) = u**3 + 5*u**2 + 4. Let p be t(-5). Factor 2 - p*i**2 - 3*i**2 + 5*i**2.
-2*(i - 1)*(i + 1)
Factor -1/2*g**2 - 1 + 3/2*g.
-(g - 2)*(g - 1)/2
Let t = 1 - -5. Suppose -3*a = -0*a - t. Suppose -g**3 + 6*g**4 + 2*g**3 - g**a - g**5 - 2*g**4 - 3*g**4 = 0. What is g?
-1, 0, 1
Let d(u) = 129*u**4 - 150*u**3 - 59*u**2 + 60*u + 16. Let j(p) = -128*p**4 + 150*p**3 + 58*p**2 - 60*p - 17. Let v(t) = 3*d(t) + 4*j(t). Factor v(k).
-5*(k - 1)**2*(5*k + 2)**2
Let r(i) = i**2 + 9*i + 3. Let t(v) = v**2 + 13*v + 5. Let x(