5 + 4/3*r**3 - 8/9*r**2 + z - 8/9*r**4 + 2/9*r.
2*r*(r - 1)**4/9
Let m = 1240 + -1240. Find d, given that 1/3*d + m - 1/6*d**3 - 1/6*d**2 = 0.
-2, 0, 1
Let p(o) be the first derivative of -o**6/360 + o**5/90 - o**4/72 - 3*o**2/2 - 3. Let s(u) be the second derivative of p(u). Suppose s(w) = 0. Calculate w.
0, 1
Let u(x) = -x**3 - 2*x**2 + 4*x + 4. Let l be u(-3). Let v be l + 1 - 3/2. Let 0 - v*j**2 + 0*j = 0. Calculate j.
0
Let y = -3 + 3. Suppose 4*l - 30 - 2 = y. Let x(f) = -7*f**3 - f**2 - 7*f - 5. Let r(a) = 11*a**3 + 2*a**2 + 11*a + 8. Let h(s) = l*x(s) + 5*r(s). Factor h(c).
-c*(c - 1)**2
Let z(j) be the first derivative of j**5/40 + 3*j**4/32 - j**2/4 - 7. Find q, given that z(q) = 0.
-2, 0, 1
Let f(y) = -y**3 + y**2 - y - 1. Let r(j) = 5*j**3 - 4*j**2 + 3*j + 4. Let u(h) = -4*f(h) - r(h). Determine v so that u(v) = 0.
-1, 0, 1
Let r(y) be the third derivative of 0*y + 0*y**3 + 0 + 2*y**2 + 1/12*y**4 + 1/60*y**5. Find p such that r(p) = 0.
-2, 0
Let g(v) be the first derivative of -v**6/40 + v**5/20 + v**4/8 - v**3/2 + 2*v**2 - 4. Let s(h) be the second derivative of g(h). Suppose s(p) = 0. What is p?
-1, 1
Let m = -8850 - -123491/14. Let w = m - -59/2. Find z, given that 0*z - w*z**2 + 2/7 = 0.
-1, 1
Let a(s) = -s**3 + 2*s**2 + 5*s - 5. Let b be a(3). Let n be b/(((-14)/(-36))/1). Let -n*h + 24/7*h**2 - 10/7*h**3 + 4/7 = 0. Calculate h.
2/5, 1
Let a(m) be the second derivative of -5*m**4/8 + 3*m**3/4 + 3*m**2/2 - 6*m. Find t such that a(t) = 0.
-2/5, 1
Let p = 485/2 - 242. What is v in -p*v + 0 - 1/2*v**2 = 0?
-1, 0
Let i(g) = g**2 - 4*g - 1. Let n be i(5). What is k in 2*k**4 + 6*k + 6*k**3 + n*k**2 - 6*k = 0?
-2, -1, 0
Let g(l) be the first derivative of -l**6/10 + 3*l**5/10 - l**4/4 + l - 1. Let z(m) be the first derivative of g(m). Factor z(u).
-3*u**2*(u - 1)**2
Let m(w) be the second derivative of w**4/12 + 5*w**3/6 + 3*w**2 - 52*w. Let m(d) = 0. What is d?
-3, -2
Suppose 3*q + 0*q + 9 = 0. Let o be (2 + q)/(1/(-2)). Let o - 4*h**2 + 2*h**2 + 3*h + 3*h**2 = 0. Calculate h.
-2, -1
Suppose -z + 0*z = -1. Let n = z + 1. Find a, given that 1/2*a**5 + 0*a - 1/2*a**3 - 1/2*a**n + 1/2*a**4 + 0 = 0.
-1, 0, 1
Let b(y) be the third derivative of -y**7/10080 - y**6/1440 - y**5/480 + y**4/12 + 7*y**2. Let a(u) be the second derivative of b(u). Factor a(z).
-(z + 1)**2/4
Suppose 0 = -3*q + 9, -3*z + 5*z = 3*q - 3. Let n(m) be the third derivative of 0 + 1/60*m**5 - 2*m**2 + 1/6*m**z + 0*m + 1/12*m**4. Factor n(v).
(v + 1)**2
Let t be 11/(11/6) - -1. Solve 3*j**2 + t - 13 - 7*j + 4*j = 0 for j.
-1, 2
Let y be ((-16)/56)/((-3)/7). Let 0 - y*w**2 - 2/3*w = 0. What is w?
-1, 0
Suppose -3*b + 2*b = 0. Suppose 6*n - 5*n = b. Factor -6*x**3 - 9/2*x**2 - 5/2*x**4 + n - x.
-x*(x + 1)**2*(5*x + 2)/2
Let w(n) be the first derivative of n**3/18 - n**2/3 + n/2 + 3. Suppose w(x) = 0. Calculate x.
1, 3
Suppose 54*l - 29*l = -45*l. Determine i, given that -6/7*i**5 - 20/7*i**3 - 4/7 + 20/7*i**4 + l*i**2 + 10/7*i = 0.
-2/3, 1
Let j(c) = -c**3 - 2*c**2 + c - 3. Suppose -3 = -f + 2*f. Let d be j(f). Factor -2*s**3 + 4*s**4 - 5*s**d + 6*s + 2*s**2 - 5*s.
s*(s - 1)**2*(4*s + 1)
Let v = 13 - 9. Suppose 0*y**2 + 8 + y**2 - 7*y**2 - 2*y**v - 8*y**3 + 8*y + 0*y**2 = 0. Calculate y.
-2, -1, 1
Let f(o) = -4*o**3 + o**2 + o + 1. Let u be f(-1). Factor 2*h**5 - u*h**3 + 2*h**4 + 3*h**3 + 0*h**4 - 2*h**2.
2*h**2*(h - 1)*(h + 1)**2
Factor -10*c**2 - c + 2*c + 20*c**2 - 11*c**2.
-c*(c - 1)
Let u = -16 + 43. What is l in 0*l**3 - 6*l**2 + u - 21 - 3*l + 3*l**3 = 0?
-1, 1, 2
Let c be 1 + (3/(-15) - 18/(-15)). Let z(f) be the third derivative of 1/15*f**5 + 4*f**c - 1/45*f**6 + 1/9*f**3 - 1/9*f**4 + 1/315*f**7 + 0 + 0*f. Factor z(r).
2*(r - 1)**4/3
Suppose -49 = -5*i - 19. Suppose -3*c + m - 1 = -i*c, -2*c - 6 = 2*m. Solve 0*y**2 + 2*y**3 + 2*y**3 - 2*y**4 - 2*y**c = 0 for y.
0, 1
Let t(z) be the second derivative of z**4/6 + 2*z**3 + 9*z**2 - 8*z. Factor t(o).
2*(o + 3)**2
Let b(r) be the third derivative of r**10/302400 - r**8/40320 + r**5/60 - r**2. Let s(q) be the third derivative of b(q). Factor s(n).
n**2*(n - 1)*(n + 1)/2
Let f(h) = h**2 - 6*h + 6. Let t be f(6). Let m be 20*1/t - 1. Factor 2/3 - 4/3*p**2 - m*p.
-(p + 2)*(4*p - 1)/3
Factor -5/3*p**2 - 80/3 - 40/3*p.
-5*(p + 4)**2/3
Let i(v) be the second derivative of -7*v + 9*v**2 + 2*v**3 + 1/6*v**4 + 0. Let i(w) = 0. What is w?
-3
Let j(m) be the first derivative of m**8/13440 - m**7/2240 + m**6/960 - m**5/960 - 3*m**3 - 4. Let g(k) be the third derivative of j(k). Solve g(i) = 0 for i.
0, 1
Let l(x) be the first derivative of -4 - 1/18*x**3 + 0*x**2 + 1/6*x. Factor l(a).
-(a - 1)*(a + 1)/6
Let f(m) be the third derivative of m**5/60 + 2*m**2. Factor f(u).
u**2
Suppose 0 = -h + 4*x + 25, -h - x = -4*x - 21. Let k be (1/h)/(2/6). Factor 1/2*r**4 - 1/2*r + k*r**3 - 1/3*r**2 + 1/6*r**5 - 1/6.
(r - 1)*(r + 1)**4/6
Let o = 26/9 - 49/18. Factor 1/3*c**4 - 1/2*c**2 + 1/6 - o*c + 1/6*c**3.
(c - 1)*(c + 1)**2*(2*c - 1)/6
Let g(d) be the first derivative of 3*d**5/10 + 3*d**4/2 + 3*d**3 + 3*d**2 + 3*d/2 - 1. Factor g(j).
3*(j + 1)**4/2
Let h(b) be the third derivative of 7*b**8/96 + b**7/20 - b**6/10 + b**5/30 - 6*b**2. Suppose h(a) = 0. What is a?
-1, 0, 2/7
Let g(f) be the third derivative of f**8/840 - f**7/175 + f**6/150 - 17*f**2. Solve g(r) = 0 for r.
0, 1, 2
Let n(m) = -m**5 - m**4 + m**3 + m**2 - m. Let a(o) = 2*o**5 + 6*o**4 - 5*o**3 - 3*o**2 + 3*o. Let z(t) = -a(t) - 3*n(t). Find q such that z(q) = 0.
0, 1, 2
Suppose 0 = -2*z + 7*z - 20. Let y(c) be the first derivative of -4/27*c**3 + 1/27*c**6 + 4/45*c**5 + 1 + 0*c**z + 0*c - 1/9*c**2. Find s such that y(s) = 0.
-1, 0, 1
Let u(m) = m**2 - 3*m - 3. Let q be u(5). Let z be (-2)/(-8)*14/q. Factor -1/2*o**2 - z*o - 1/6*o**3 - 1/6.
-(o + 1)**3/6
Let w(b) be the second derivative of -1/21*b**7 + 3/10*b**5 + 0*b**2 - 2*b + 0*b**6 + 1/3*b**4 + 0 + 0*b**3. Find k, given that w(k) = 0.
-1, 0, 2
Let k(r) be the first derivative of -r**4/22 - 4*r**3/33 + 3*r**2/11 + 30. Solve k(z) = 0 for z.
-3, 0, 1
Let t(z) be the first derivative of -z**3 + 9*z**2/2 - 6*z + 8. Factor t(k).
-3*(k - 2)*(k - 1)
Suppose -2/3*c**4 + 0*c + 0*c**2 + 0 + 2/3*c**5 - 4/3*c**3 = 0. Calculate c.
-1, 0, 2
Suppose -11*p + 4*p + 14 = 0. Let n(m) be the first derivative of m**p + 2/3*m**3 - 2*m - 3 - 1/2*m**4. Determine s so that n(s) = 0.
-1, 1
Let l(q) = -3*q**3 + 5*q**2 - 6*q + 4. Let u(w) = w**3 - 2*w**2 + 3*w - 2. Let j(x) = -4*l(x) - 10*u(x). Determine a, given that j(a) = 0.
-2, 1
Let q(u) = 3*u**2 + 8*u - 3. Suppose 5*p = 22 + 3. Let w(t) = -4*t**2 - 8*t + 2. Let k(i) = p*w(i) + 6*q(i). Suppose k(g) = 0. Calculate g.
2
Let t(k) be the second derivative of 1/6*k**4 + 0 + 1/42*k**7 - 2*k + 0*k**2 + 0*k**5 - 1/15*k**6 - 1/6*k**3. Solve t(x) = 0 for x.
-1, 0, 1
Let l(g) = 6*g**5 + 18*g**4 - 28*g**2 - 8*g + 6. Let a(x) = 31*x**5 + 90*x**4 - x**3 - 141*x**2 - 41*x + 29. Let j(z) = -4*a(z) + 22*l(z). Solve j(f) = 0 for f.
-4, -1, 1/2, 1
Suppose -73 = 8*l - 97. Determine a so that -2/3*a**l + 1/3*a**4 - 1/3 + 0*a**2 + 2/3*a = 0.
-1, 1
Let k(g) = -2*g**4 - 22*g**3 - 54*g**2 - 46*g - 14. Let n(i) = -i**4 - 21*i**3 - 55*i**2 - 45*i - 13. Let v(y) = -3*k(y) + 2*n(y). Factor v(x).
4*(x + 1)**2*(x + 2)**2
Let d(k) = -k**3 - 6*k**2 + k + 8. Let t = 14 - 20. Let c be d(t). Factor 2/3*s - 1/3*s**c - 1/3.
-(s - 1)**2/3
Determine g so that -10/13*g**4 + 0*g + 0 + 16/13*g**3 - 8/13*g**2 + 2/13*g**5 = 0.
0, 1, 2
Let d(a) = -a**3 - 3*a**2 - a + 1. Let q be d(-3). Suppose -8 = -q*g, g + 1 = -k + 3*g. Factor w**2 - w + 0*w**2 - 3*w**2 + 2*w**k - 3*w.
2*w*(w - 2)*(w + 1)
Let h = 524/9 + -58. Factor -2/9 + h*d - 2/9*d**3 + 2/9*d**2.
-2*(d - 1)**2*(d + 1)/9
Let n(i) be the first derivative of 9*i**4/20 - i**3/5 - i**2/2 - i/5 + 2. Factor n(d).
(d - 1)*(3*d + 1)**2/5
Let o(c) = -21*c + 24. Let n(v) = -v**2 + 20*v - 25. Let k(x) = 3*n(x) + 2*o(x). Factor k(t).
-3*(t - 3)**2
Let l(u) be the third derivative of 0 + 0*u**4 + 0*u + 9*u**2 + 0*u**3 - 1/60*u**6 - 1/30*u**5. What is v in l(v) = 0?
-1, 0
Let g = 6 + -7. Let a(z) = 2*z**3 + 6*z**2 + 12*z - 4. Let i(d) = d - 1. Let y(t) = g*a(t) + 6*i(t). Find s, given that y(s) = 0.
-1
Let k(q) = -q**3 - q**2 - 1. Let w be k(-2). Factor -9*t - 13*t**2 - 6 + 13*t**2 + w*t**3.
3*(t