 derivative of 0 + 0*g + 3/40*g**5 - 11*g**2 + 0*g**3 - 1/112*g**8 - 3/140*g**7 + 1/16*g**4 + 1/80*g**6. Solve k(r) = 0 for r.
-1, -1/2, 0, 1
Let t(z) = 2*z**5 - 12*z**4 + z**3 + 41*z**2 - 17*z + 5. Let o(m) = m**5 - m**3 + m**2 + 2*m + 1. Let l(f) = 5*o(f) - t(f). Factor l(i).
3*i*(i - 1)**2*(i + 3)**2
Suppose -3*q = -3, 2*q - 5 = -3*z + 3. Let u be 1/9*2*z. Find a such that -u + 2/9*a - 2/9*a**3 + 4/9*a**2 = 0.
-1, 1, 2
Let m(d) be the second derivative of -d**4/8 - 297*d**3/2 - 264627*d**2/4 + 430*d. Factor m(h).
-3*(h + 297)**2/2
Suppose 10/19*k**3 + 14/19*k - 26/19*k**2 + 0 + 2/19*k**4 = 0. Calculate k.
-7, 0, 1
Let g = -803/12 + 67. Let q(w) be the second derivative of 11/48*w**4 + 5*w + 7/120*w**6 + 0 - g*w**3 + 0*w**2 - 1/5*w**5. Factor q(t).
t*(t - 1)**2*(7*t - 2)/4
Suppose -5*f = -2*w - 24, 0 = -2*w + w - 2. Suppose -f*i + 27 = 3. Find t such that -t + 4*t**3 - 7*t**3 + 6 + i*t + 4*t = 0.
-1, 2
Let x(z) = -6*z**2 - 20*z + 19. Let p(y) = -10*y**2 + 2*y**2 - 40*y - 4*y**2 - 42 + 79. Let f(v) = -3*p(v) + 5*x(v). Factor f(w).
2*(w + 4)*(3*w - 2)
Factor -5*f + 25*f**2 + 4 + 28*f**2 + 25*f**2 - 77*f**2.
(f - 4)*(f - 1)
Let z be 180/(4 - 2)*(0 - -1). Let j be 2 + 6/(z/(-25)). Find d, given that -2/3 - d - j*d**2 = 0.
-2, -1
Let h(w) be the second derivative of -w**6/30 - w**5/5 + w**4/6 + 2*w**3 + 14*w**2 + 41*w. Let b(l) be the first derivative of h(l). Factor b(t).
-4*(t - 1)*(t + 1)*(t + 3)
Let p(l) be the second derivative of l**5/110 + l**4/6 - 56*l**3/33 + 60*l**2/11 - 13*l - 2. Let p(y) = 0. What is y?
-15, 2
Let v be 3/(0 + (-1)/(-2)). Let z be (-10 + 2)*v/(-12). Solve z + 0 - 76*g + 50*g + 22*g**2 = 0 for g.
2/11, 1
Suppose -5*n - 2*t - 586 = -3*n, 3*t - 1441 = 5*n. Let d = 583/2 + n. What is r in 3/2*r + 33/2*r**3 + d - 27/2*r**2 - 6*r**4 = 0?
-1/4, 1
Let b = -1 + 3. Let i = 189 + -184. Factor -9*y**3 - 3*y**i - 3*y**b + 5*y**4 - 11*y**4 - 3*y**4.
-3*y**2*(y + 1)**3
Let w = 2602 + -2592. Let v(f) be the third derivative of -1/8*f**4 + 1/120*f**5 + 0 - w*f**2 + 3/4*f**3 + 0*f. Factor v(s).
(s - 3)**2/2
Suppose a - 8*a = -6*a. Let l(c) be the third derivative of -7*c**2 + 2/105*c**7 + 0*c**5 - 1/20*c**6 + 0 + 0*c**3 + 1/12*c**4 + a*c. Let l(h) = 0. What is h?
-1/2, 0, 1
Let p = -7554/187 + 696/17. Factor 6/11*o**3 + 0 + 2/11*o - 2/11*o**4 - p*o**2.
-2*o*(o - 1)**3/11
Let r(f) be the third derivative of -2*f**7/35 + 17*f**6/30 - 28*f**5/15 + 2*f**4 + 13*f**2 - 3. Factor r(m).
-4*m*(m - 3)*(m - 2)*(3*m - 2)
Let a(y) be the second derivative of -y**7/105 + 27*y**5/50 - 9*y**4/5 - 6*y + 10. Solve a(f) = 0 for f.
-6, 0, 3
Let n = 9/275 + 156/275. Factor -3/5*y + 3/5*y**3 + 3/5*y**4 + 0 - n*y**2.
3*y*(y - 1)*(y + 1)**2/5
Factor -124/3*r + 4/3*r**3 - 32/3*r**2 - 88/3.
4*(r - 11)*(r + 1)*(r + 2)/3
Solve -17/5*b + 12 - 1/5*b**2 = 0.
-20, 3
Let m(l) be the second derivative of -4*l**3 + 4*l**2 + 13/6*l**4 + 1/15*l**6 - 3/5*l**5 + 0 + 7*l. Solve m(i) = 0 for i.
1, 2
Let n = -1564 + 4696/3. Determine l, given that -4/3*l**3 + 1/3*l**4 + 0*l + 0 + n*l**2 = 0.
0, 2
Suppose 202 = t - 4*m, -m + 1 + 3 = 0. Solve -t + 218 - 2*n**2 - n**2 - 3*n = 0 for n.
-1, 0
Let r be (12/30)/((-1)/(-5)). Suppose -r*u = -8, -8 = 4*l - 6*u + 2*u. Determine h so that 4*h - 2*h - 2*h**3 - 29*h**l + 29*h**2 = 0.
-1, 0, 1
Let s(i) be the second derivative of i**4/28 - i**3/2 - 27*i**2/7 + 4*i + 34. Solve s(w) = 0.
-2, 9
Let i be (0*6/30)/((-132)/11 + 8). Factor 4/9*u - 4/9*u**3 + i + 0*u**2.
-4*u*(u - 1)*(u + 1)/9
Let m(v) be the first derivative of -v**5/40 - 5*v**4/32 + v**3/4 + 57. Determine f so that m(f) = 0.
-6, 0, 1
Let j(r) be the third derivative of -5*r**8/84 - 32*r**7/105 + r**6/15 + 16*r**5/15 + r**4/2 - 10*r**2. Solve j(x) = 0 for x.
-3, -1, -1/5, 0, 1
Let r(y) = y**2 - y - 9. Let p be r(4). Factor 25*d + 4*d**2 + 3*d**3 + d**p - 25*d.
4*d**2*(d + 1)
Let t(y) = -y**2 - 16*y - 11. Let i = -37 + 22. Let x be t(i). Solve 3*q**2 + 3*q**4 + 3*q**2 + x*q**3 + 5*q**3 = 0 for q.
-2, -1, 0
Solve -87*h**2 - 31567*h + 24*h**3 + 31315*h - 35 - 13*h**2 - 37 = 0.
-3/2, -1/3, 6
Solve 18*r**2 + 24 + 3/2*r**3 - 3/2*r**4 - 42*r = 0.
-4, 1, 2
Let c = 14 - 12. Let u = 1291/21 + -181/3. Determine f so that 10/7*f + 4/7 + 2/7*f**3 + u*f**c = 0.
-2, -1
Let v(x) be the third derivative of -x**6/30 + x**5/15 + 2*x**4/3 - 8*x**3/3 + 3*x**2 - 43. Factor v(s).
-4*(s - 2)*(s - 1)*(s + 2)
Let r(g) = 22*g + 22. Let m be r(-1). Factor m + 40/9*l**2 + 2*l**3 + 8/9*l.
2*l*(l + 2)*(9*l + 2)/9
Let d be (-50)/(25/(-5)) + 1. Suppose -a + 8 = 2*u, -3*u + 1 + d = a. Factor -10/3*z**5 + 0*z**2 + 0*z + 4/3*z**3 + 2*z**4 + a.
-2*z**3*(z - 1)*(5*z + 2)/3
Let a be (-182)/(-78) - (24/(-9))/4. Let y(s) be the second derivative of 0 - 11/4*s**4 + 0*s**2 + 5*s + s**a + 27/20*s**5. Factor y(z).
3*z*(z - 1)*(9*z - 2)
Let c(j) = 9*j**4 - 18*j**3 + 39*j**2 - 30*j - 6. Let x(d) = 8*d**4 - 19*d**3 + 41*d**2 - 30*d - 5. Let g(z) = -5*c(z) + 6*x(z). Factor g(m).
3*m*(m - 5)*(m - 2)*(m - 1)
Let i(n) = -5*n - 18. Let z be i(-4). What is g in 0*g**z + 7*g + 11*g - 12*g - 8*g**2 + 2 = 0?
-1/4, 1
Let f(s) be the first derivative of s**6/50 + 3*s**5/20 + 3*s**4/10 - 2*s**3/5 - 12*s**2/5 - 19*s - 22. Let o(q) be the first derivative of f(q). Factor o(k).
3*(k - 1)*(k + 2)**3/5
Suppose 6 = -2*y + 4*y. Suppose 2*o - 8 = d - 0*d, -5*o + 3*d + 21 = 0. Factor -2 + 3 + n**o + 2*n + y*n**2 + n.
(n + 1)**3
Let s(a) be the second derivative of -a**4/24 + a**3/48 + 25*a - 1. Determine y so that s(y) = 0.
0, 1/4
Let l = -113 - -116. Let a(t) be the first derivative of -2/3*t**3 + 2/5*t**5 - l + 0*t - 1/3*t**6 + 1/2*t**4 + 0*t**2. Factor a(y).
-2*y**2*(y - 1)**2*(y + 1)
Let f(v) be the third derivative of -v**10/604800 + v**8/26880 - v**7/10080 - v**5/4 + 43*v**2. Let o(k) be the third derivative of f(k). Factor o(l).
-l*(l - 1)**2*(l + 2)/4
Let p(q) = 19*q**3 + 2*q**2 - 4. Let m(s) = -s**3 + 1. Suppose 2*b + 7 = 5*f, -3*f = -3*b - b + 7. Let x(w) = b*m(w) + p(w). Determine u so that x(u) = 0.
-2/15, 0
Let f(c) be the second derivative of c**7/70 + c**6/20 - c**5/20 - c**4/4 + 11*c**2/2 - 18*c. Let v(o) be the first derivative of f(o). Factor v(p).
3*p*(p - 1)*(p + 1)*(p + 2)
Let o = 407 + -651. Let z = -1949/8 - o. Suppose -1/4 - 1/8*v**2 - z*v = 0. What is v?
-2, -1
Let y(j) be the first derivative of j**6/27 - 2*j**5/15 + j**4/18 + 2*j**3/9 - 2*j**2/9 + 11. Let y(p) = 0. What is p?
-1, 0, 1, 2
Let m(o) = -o**2 + 12*o - 15. Let f be m(12). Let c be f/10 - (-122)/4. Factor 3*l - 3*l**2 + 3*l**4 - 3*l**3 + 29 - c.
3*l*(l - 1)**2*(l + 1)
Let b(z) = -z**3 - 19*z**2 - 16*z + 36. Let k be b(-18). Let m(q) be the first derivative of k*q**2 - 7 + 3/4*q**3 - q. Let m(y) = 0. Calculate y.
-2/3, 2/3
Let b(d) be the second derivative of -2*d**6/15 + 9*d**5 + 47*d**4/3 - 30*d**3 - 92*d**2 - 811*d. Solve b(w) = 0 for w.
-1, 1, 46
Let n(u) = u**3 - 18*u**2 + 32*u. Let i be n(16). Factor i*d**3 - 15*d + d**3 + 14*d.
d*(d - 1)*(d + 1)
Let v(w) be the third derivative of -w**5/390 - w**4/156 + 2*w**3/39 + 8*w**2 + 42*w. Suppose v(o) = 0. Calculate o.
-2, 1
Let c(q) = q**2 - 19*q + 20. Let r be c(17). Let u be 8/40*(r/(-4) - 1). Solve 0*l + 1/4 + 1/4*l**4 - u*l**2 + 0*l**3 = 0.
-1, 1
Suppose 0*i - 31*i**2 + 20*i + 28*i + 3*i**4 - 5*i**2 = 0. Calculate i.
-4, 0, 2
Let t(m) be the second derivative of -m**5/20 - m**4/48 + 2*m**3/3 + m**2/2 + 115*m. Factor t(j).
-(j - 2)*(j + 2)*(4*j + 1)/4
Solve -109/3*r**2 - 20*r**3 - 5/2 - 52/3*r + 3/2*r**4 = 0.
-1, -1/3, 15
Let l be -9*((-16)/12 - -2). Let w be 0 + (0 - l) + -3. Factor -6*s**3 + s**3 + s**w - 16*s**2 - 30*s + 18*s.
-4*s*(s + 1)*(s + 3)
Let b be (-35 - -1)*3/6. Let r = b + 28. Determine y, given that r*y**4 + 2 - 4*y**4 - 3*y - 7*y**4 - y**5 - 2*y**2 + 4*y**3 = 0.
-2, -1, 1
Let s(t) = -4*t**4 - 44*t**3 - 92*t**2 + 4. Let o(g) = -8*g**4 - 88*g**3 - 189*g**2 + 9. Let d(w) = 4*o(w) - 9*s(w). Factor d(m).
4*m**2*(m + 2)*(m + 9)
Let u(l) be the third derivative of -l**5/270 - 77*l**4/54 - 5929*l**3/27 - 209*l**2 + 2*l. Factor u(a).
-2*(a + 77)**2/9
Let v(m) = -m**3 - 9*m**2 + 10*m + 4. Let l be v(-10). Suppose -6 = -2*r, 2*r = -n - l + 14. Find a, given that -n*a**2 + 4*a**4 + 0*a**4 + 0*a**4 = 0.
-1, 0, 1
Let g(h) be the second derivative of -h**7/42 + h**6/8 + h**5/3 + 6*h**2 - 38*h. Let s(t) be t