/6*j - 1/30*j**5. Factor g(a).
-(a - 1)**2*(a + 1)**3/6
Factor 4*x**4 + x**3 - 123*x**2 + 23*x**3 - 3*x**3 + 99*x - x**4.
3*x*(x - 3)*(x - 1)*(x + 11)
Suppose -1970*l - 18 = -1976*l. Let w be 8/6 - (-1 - 0). Factor w*n**2 + 2/3*n - l*n**3 + 0.
-n*(n - 1)*(9*n + 2)/3
Let j(l) be the second derivative of 1/72*l**4 + 0 + 1/720*l**6 - 1/144*l**5 + 0*l**2 + 2*l + l**3. Let u(h) be the second derivative of j(h). Factor u(m).
(m - 1)*(3*m - 2)/6
Let k(t) = -6*t**2 - 99*t + 145. Let d(q) = q**2 + 20*q - 30. Let n(o) = 11*d(o) + 2*k(o). Determine v, given that n(v) = 0.
2, 20
Let u be (20/(-6))/((-6)/9). Let m(z) be the second derivative of 9*z + 0 + 1/10*z**u + 0*z**2 + 1/3*z**4 + 1/3*z**3. Factor m(q).
2*q*(q + 1)**2
Let y(g) = 7*g**2 - g. Let x be y(-1). Find h such that 15*h + x*h**2 + 138 - 132 + h**2 = 0.
-1, -2/3
Suppose 49*p + 16 = 51*p - 3*w, -2 = -2*p - 4*w. Let 13/6*i**3 + 10/3*i**2 + 3/2*i**p + 2/3*i + 0 - 5*i**4 = 0. Calculate i.
-1/3, 0, 2
Let y(h) be the third derivative of -h**7/8820 + 13*h**6/1260 - 169*h**5/420 + 4*h**4/3 + 13*h**2. Let x(i) be the second derivative of y(i). Factor x(u).
-2*(u - 13)**2/7
Let t(y) be the third derivative of -y**9/2240 - 11*y**8/2240 - y**7/42 - y**6/15 - y**5/20 + 12*y**2. Let r(p) be the third derivative of t(p). Factor r(h).
-3*(h + 1)*(3*h + 4)**2
Let w(b) = b**3 + 12*b**2 + 3. Let u be w(-12). Solve -m**u - 3*m**3 + 16*m**2 - 24*m**2 - 4*m = 0 for m.
-1, 0
Let k(g) = -g**3 - 19*g**2 - 12*g + 6. Let j(q) = -9*q**2 - 6*q + 3. Let x(d) = -13*j(d) + 6*k(d). Let x(y) = 0. Calculate y.
-1, 1/2, 1
Let 106/5*h**3 - 24/5*h**4 + 216/5*h + 2/5*h**5 - 44*h**2 - 16 = 0. Calculate h.
1, 2, 5
Let h = 219 + -377. Let y = h + 158. Suppose 1/3*w**3 - 1/3*w + 0 + y*w**2 = 0. What is w?
-1, 0, 1
Let t = 13 + -11. Suppose 0 = -5*z - t*g - 9 + 1, g = 2*z - 4. Solve -m + z*m**3 - 3*m**4 + 3*m**3 - 2*m + 9*m**2 - 10 + 4 = 0 for m.
-1, 1, 2
Let f(u) be the first derivative of 0*u**3 - 18/35*u**5 + 0*u**2 - 10 - 1/3*u**6 + 0*u - 1/7*u**4. Suppose f(n) = 0. What is n?
-1, -2/7, 0
Suppose -g + u + u + 1 = 0, -5*u - 4 = -4*g. Let v be (15/(-180))/(g/(-2)). What is o in -1/3 + v*o - 1/6*o**3 + 1/3*o**2 = 0?
-1, 1, 2
Factor 40/9*y**3 + 472/9*y**2 + 160*y + 1/9*y**4 + 144.
(y + 2)**2*(y + 18)**2/9
Let x = 16 + -12. Suppose 0 = -x*m - 5 + 25. Find v, given that -v - 4*v - 10*v - m + 0*v + 20*v**2 = 0.
-1/4, 1
Let -33/7 - 6/7*d**2 + 69/7*d = 0. What is d?
1/2, 11
Let x(s) be the second derivative of s**7/42 - 4*s**6/15 + 9*s**5/10 - 4*s**4/3 + 5*s**3/6 - 28*s. Factor x(y).
y*(y - 5)*(y - 1)**3
Let v be 47/423 + (-551)/(-9) - -4. What is y in 4/3*y**2 - 56/3*y + v = 0?
7
Factor -45/4*w + 1/4*w**3 + 21/4*w**2 + 23/4.
(w - 1)**2*(w + 23)/4
Let i(f) be the first derivative of 2*f**5/15 - 5*f**4/3 + 32*f**3/9 + 35. Solve i(b) = 0.
0, 2, 8
Solve 128*v**2 - 40*v**4 + 40 + 24 - 90 + 188*v + 37 - 24*v**3 - 4*v**5 + 61 = 0 for v.
-9, -1, 2
Let r be (-144)/108*(-15)/50. Solve 2/5*a**2 - r*a + 0 = 0.
0, 1
Let o(j) = -4*j**3 + 16*j**2 + 36*j. Let t(i) = i**3 - 5*i**2 - 12*i. Suppose 24 = -3*a - 3*d, -5*d = 2*a - 2 + 33. Let w(n) = a*o(n) - 8*t(n). Factor w(b).
4*b*(b - 3)*(b + 1)
Let o(x) = 1 - 11*x**2 + 4*x + 7*x**2 + x**3 - 4 - 2*x**3. Let i be o(-5). Factor -8/5*q - 194/5*q**3 - 72/5*q**i + 0 - 144/5*q**4 - 32/5*q**5.
-2*q*(q + 2)**2*(4*q + 1)**2/5
Let l(t) be the third derivative of t**8/5376 - t**7/5040 - t**6/576 + t**5/240 - t**4/8 + 7*t**2. Let y(m) be the second derivative of l(m). Factor y(d).
(d - 1)*(d + 1)*(5*d - 2)/4
Let d = 138 - 135. Factor 4*w**d - 17*w**4 + 9*w**2 - 7*w**3 - 5*w + 0*w + 16*w**4.
-w*(w - 1)**2*(w + 5)
Let k = -114/11 - -1570/143. Factor -2/13*j**2 + k + 6/13*j.
-2*(j - 4)*(j + 1)/13
Suppose -9*r**2 + 3/2*r**3 + 0 - 60*r = 0. What is r?
-4, 0, 10
Solve -26/9*t**3 + 0 - 10/9*t**4 - 14/9*t**2 + 2/9*t**5 + 0*t = 0.
-1, 0, 7
Let c be 1*9/(-2)*-2. Find m such that -4*m + 21*m**2 + 16*m - 3 - c + 24*m = 0.
-2, 2/7
Let t(a) be the second derivative of a**7/168 - a**6/30 + 3*a**5/80 + 599*a. Factor t(n).
n**3*(n - 3)*(n - 1)/4
Determine k, given that 1/4*k**3 - 3/4*k**4 - 1/4*k**5 + 0*k + 3/4*k**2 + 0 = 0.
-3, -1, 0, 1
Let w(u) be the first derivative of -u**6/6 - u**5/5 + 5*u**4 - 125. Determine o, given that w(o) = 0.
-5, 0, 4
Let b(c) be the third derivative of -c**6/60 - c**4/8 + c**3/6 + 12*c**2. Let a(n) = -n**3 - n**2 - 2*n + 2. Let i(x) = 3*a(x) - 2*b(x). Factor i(l).
(l - 2)**2*(l + 1)
Suppose 4 = 22*t + 4. Let c(v) be the third derivative of 0*v**3 - 1/30*v**5 + 0 + 1/120*v**6 + 1/210*v**7 + v**2 + 0*v**4 + t*v. Find o, given that c(o) = 0.
-2, 0, 1
Let l(j) be the first derivative of -j**6/24 + 3*j**4/16 - j**3/6 - 42. Let l(z) = 0. What is z?
-2, 0, 1
Let v(j) = -j - 7*j + 14*j - 7*j - 1. Let m(b) = b**2 - 1. Let i(t) = -3*m(t) - 21*v(t). Determine r, given that i(r) = 0.
-1, 8
Let f(n) be the second derivative of 0*n**2 + 0 + 1/150*n**6 + 1/20*n**5 + 3*n + 2/15*n**3 + 2/15*n**4. Suppose f(j) = 0. Calculate j.
-2, -1, 0
Suppose -j - 3*y = -55, -2*j = -4*j - 2*y + 102. Factor -5*l**4 + 3*l**3 + j*l - 49*l + 12*l**3 - 10*l**2.
-5*l**2*(l - 2)*(l - 1)
Let z(k) be the first derivative of -16*k**5/35 + 11*k**4/14 - 2*k**3/7 - 251. Factor z(m).
-2*m**2*(m - 1)*(8*m - 3)/7
Let l(z) be the second derivative of z**6/180 - 2*z**5/15 + 31*z**4/36 - 20*z**3/9 + 11*z**2/4 - z - 243. Find f such that l(f) = 0.
1, 3, 11
Let w = -15 + 18. Let v = -191 + 191. Factor v*r**2 - 1/6*r + 0 + 1/6*r**w.
r*(r - 1)*(r + 1)/6
Let f(q) = 828*q**2 + 2*q. Let j be f(-1). Factor -826*d**2 - 8*d**4 - 12*d**3 + j*d**2 + 4*d**5.
4*d**3*(d - 3)*(d + 1)
Let i be (-5 - 46/(-8))*8. Let m be (-10)/(20/3)*(-8)/i. Solve 3*g**m + 6/5 + 21/5*g = 0 for g.
-1, -2/5
Factor 0*q**2 - 10*q**2 - 143*q**5 - 15*q**3 + 148*q**5.
5*q**2*(q - 2)*(q + 1)**2
Let f(q) be the second derivative of -1/24*q**4 + 0*q**3 + 1/80*q**5 + 0*q**2 - 30*q + 0 + 1/120*q**6. Determine o so that f(o) = 0.
-2, 0, 1
Let v(p) = -2*p**2 - 3*p - 3. Let x be v(-2). Let q be 32/40*x/(-2). Let 4/11*t**3 + 0*t + 0 - 4/11*t**5 + 2/11*t**q - 2/11*t**4 = 0. Calculate t.
-1, -1/2, 0, 1
Let u(y) be the third derivative of 5/2*y**3 - 25/24*y**4 - 1/42*y**7 - 1/6*y**5 + 0 + 1/4*y**6 + 13*y**2 - 5/336*y**8 + 0*y. Factor u(t).
-5*(t - 1)**3*(t + 1)*(t + 3)
Let w be 0/(-991)*(2/(-3) - -1). Factor 2/9*g**5 - 2/9*g + 4/9*g**4 - 4/9*g**2 + w + 0*g**3.
2*g*(g - 1)*(g + 1)**3/9
Let p be 40/(-140) + (-62)/(-168). Let y(o) be the first derivative of 1/6*o**2 - p*o**4 + 0*o**3 - 4 + 0*o. Determine w so that y(w) = 0.
-1, 0, 1
Determine k, given that -10/3*k**2 + 0 + 148/15*k**3 + 2/5*k**4 + 0*k = 0.
-25, 0, 1/3
What is f in -440*f**3 - 32626*f**4 + 428*f**2 + 32782*f**4 - 160*f + 1 + 15 = 0?
2/13, 2/3, 1
Factor -3*d**2 + 365*d + 182*d + d**2 - 42050 + 33*d.
-2*(d - 145)**2
What is g in -44/3*g + 8/3 - 15*g**3 + 74/3*g**2 + 3*g**4 = 0?
1/3, 2/3, 2
Let z(b) = b**2 + 7*b + 5. Let t be (7/(1 - 2))/1. Let s be z(t). Factor 3*y**5 + 3*y**5 + 0*y**5 - 7*y**s.
-y**5
Let o(c) be the third derivative of -125*c**8/336 + 85*c**7/42 - 67*c**6/24 - 17*c**5/12 + 25*c**4/6 + 10*c**3/3 + 90*c**2. Find h such that o(h) = 0.
-2/5, -1/5, 1, 2
Let k(s) = s**3 + s - 1. Let d(q) = q**4 + 2*q**3 + 9*q**2 - 5. Let n(w) = 5*d(w) - 35*k(w). Factor n(x).
5*(x - 2)*(x - 1)**3
Let s(p) be the second derivative of 0*p**4 + 0*p**2 + 0*p**6 + 1/3*p**3 + 0 - 13*p + 1/21*p**7 - 1/5*p**5. Let s(l) = 0. What is l?
-1, 0, 1
Let o = -36029 - -36029. Determine h so that 0*h**3 + 15/2*h**4 + o*h - 5/2*h**5 - 10*h**2 + 0 = 0.
-1, 0, 2
Let l(u) be the third derivative of u**6/24 + 23*u**5/12 - 65*u**4/12 - 40*u**3 - 19*u**2 - 1. Find f, given that l(f) = 0.
-24, -1, 2
Let m be (-4)/1 - (-2164)/540. Let n(r) be the second derivative of -4/27*r**3 - 2/45*r**5 + 1/9*r**4 + m*r**6 - 4*r + 0 + 1/9*r**2. Factor n(o).
2*(o - 1)**4/9
Let y(a) be the second derivative of -5/2*a**2 + 0 + 5/3*a**3 - 2*a + 5/4*a**4. Let y(s) = 0. Calculate s.
-1, 1/3
Let h(b) = b**2 - 9*b. Let t(y) = -y**2 + 5*y. Let f(n) = -6*h(n) - 11*t(n). Let r be f(-1). Factor -d**5 - 6*d**4 + 2*d**4 - r*d**3 - 4*d**2 - d + 0*d**2.
-d*(d + 1)**4
Let k = 2 - 0. Let f be ((-24)/(-36))/(0 + 1). Factor -2/3*s - f*s**k + 4/3.
-2*(s - 1)*(s + 2)/3
Let h be 12*1*-4*(-15)/48. Let u be 9/h + 3