 14*r**4/3 - 40*r**3/3 + 16*r**2 - 3*r. Find v, given that d(v) = 0.
2/3, 2
Factor -1/9*t**2 + 1/9*t + 2/9.
-(t - 2)*(t + 1)/9
Let m(x) = 20*x**2 - 20*x - 6. Let d(s) = s**2 + s + 1. Let w(g) = 4*d(g) + 2*m(g). What is n in w(n) = 0?
-2/11, 1
Let u(r) = 7*r - 6. Let x be u(8). Factor b**4 - 38*b**3 - 11*b**4 - x*b**2 - 32*b - 2*b**5 - 4*b**4 + 0*b**5 - 8.
-2*(b + 1)**3*(b + 2)**2
Find a such that 0 + 4/7*a + 9/7*a**4 - 26/7*a**3 + 4/7*a**5 + 9/7*a**2 = 0.
-4, -1/4, 0, 1
Let i = -10 - -12. Factor 4*q - 11*q**2 + 8*q**i + 0*q**3 + 5*q**3 - q**4 - 5*q**2.
-q*(q - 2)**2*(q - 1)
Suppose 3 = 3*j - 6*j. Let a be ((-2)/(-27))/(j/(-21)). Factor -a*g**4 + 0*g + 2*g**3 + 0 - 4/9*g**2.
-2*g**2*(g - 1)*(7*g - 2)/9
Factor 4/9*q**2 - 14/9*q**3 - 4/9 + 14/9*q.
-2*(q - 1)*(q + 1)*(7*q - 2)/9
Let i(c) be the third derivative of 0 - 1/100*c**6 + 1/350*c**7 + 0*c - 8*c**2 + 0*c**3 + 1/100*c**5 + 0*c**4. Find d such that i(d) = 0.
0, 1
Let v(n) be the third derivative of -n**7/7560 + n**6/1080 + n**4/12 + 2*n**2. Let p(w) be the second derivative of v(w). Find q such that p(q) = 0.
0, 2
Let l be -1*(2 - (0 - -7)). Let i(n) be the third derivative of 0*n**3 - 1/84*n**6 - 1/42*n**4 - 2*n**2 + 0*n + 0 - 1/30*n**l. Let i(u) = 0. What is u?
-1, -2/5, 0
Let c = -192967411 - -450000011195/2332. Let p = c - -1/1166. Factor -1/4 - 125/4*z**3 - 75/4*z**2 - p*z.
-(5*z + 1)**3/4
Let f(y) be the third derivative of y**5/90 - 11*y**4/18 + 121*y**3/9 - 9*y**2. Factor f(g).
2*(g - 11)**2/3
Suppose 0 = 4*t - t - 21. Let d = t + -47/7. Factor -2/7*p**3 - 4/7*p**2 - d*p + 0.
-2*p*(p + 1)**2/7
Let s(n) be the first derivative of 0*n + 2*n**2 - 3 + 2/3*n**3. Factor s(w).
2*w*(w + 2)
Suppose -5*h = -0 - 10. Let x(m) be the second derivative of 1/15*m**6 + 2*m + 1/10*m**5 + 0 + 1/63*m**7 + 0*m**h + 0*m**3 + 1/18*m**4. Factor x(g).
2*g**2*(g + 1)**3/3
Let r(c) be the third derivative of -c**8/112 - c**7/14 - c**6/4 - c**5/2 - 5*c**4/8 - c**3/2 + 6*c**2. Solve r(g) = 0.
-1
Let i(a) be the third derivative of -2*a**7/35 + 4*a**6/15 - a**5/5 - a**4/3 + 7*a**2. Factor i(j).
-4*j*(j - 2)*(j - 1)*(3*j + 1)
Let d(z) be the first derivative of -z**7/1260 - z**6/540 + z**5/90 + 2*z**3/3 - 4. Let s(k) be the third derivative of d(k). Factor s(h).
-2*h*(h - 1)*(h + 2)/3
Suppose 0 = -7*r - 1 + 15. Let i(x) be the second derivative of -2/3*x**4 + 0 - x**r + 2*x + 4/3*x**3. Suppose i(t) = 0. What is t?
1/2
Let p be ((-1)/(-2))/(1/8). Let c(l) be the second derivative of -3/8*l**2 - 1/16*l**p - 1/4*l**3 + 2*l + 0. Let c(y) = 0. Calculate y.
-1
Determine o, given that 4*o**2 + 7*o**3 - 12*o + 5*o**3 + 0*o**3 + 9*o**4 - 13*o**4 = 0.
-1, 0, 1, 3
Let j be (-20)/(-35) + (-8)/14. Let x(o) be the third derivative of -1/540*o**6 + 0*o**5 + 0 + 0*o + 1/945*o**7 + 4*o**2 + 0*o**3 + j*o**4. Factor x(q).
2*q**3*(q - 1)/9
Find x, given that 0*x + 0 + 0*x**2 - 14/3*x**4 + 10/3*x**5 + 4/3*x**3 = 0.
0, 2/5, 1
Suppose d - d + d = 0. Let c(r) be the third derivative of -1/540*r**6 + 1/54*r**4 + 1/270*r**5 + d + 0*r**3 + r**2 + 0*r. Solve c(n) = 0.
-1, 0, 2
Find l, given that 18/5 + 2/5*l**2 + 12/5*l = 0.
-3
Factor -51*l**2 + 55*l**2 + 0 - 4.
4*(l - 1)*(l + 1)
Let -8*k - 4*k**2 - 7 + 7 = 0. Calculate k.
-2, 0
Let o = 2/51 + 43/204. Determine b, given that 1/2 + o*b**2 + 3/4*b = 0.
-2, -1
Suppose 7*q = 2*q - 25. Let s = -3 - q. Determine x, given that s*x**4 - 2*x**2 - 2*x**5 + 0*x**4 + 4*x**5 - 2*x**3 = 0.
-1, 0, 1
Let l(h) be the first derivative of 2*h**5/55 + 5*h**4/22 + 4*h**3/11 - 4*h**2/11 - 16*h/11 - 7. Factor l(v).
2*(v - 1)*(v + 2)**3/11
Let z be (-7)/((-28)/(-12)) - -87. Let g be (z/(-35))/((-21)/10). Determine v, given that -14*v**3 + 48/7*v + g + 6*v**2 = 0.
-2/7, 1
Let z(f) be the first derivative of -1/24*f**6 - 1/12*f**3 + 1 + 1/16*f**4 + 0*f + 1/20*f**5 + 0*f**2. Determine w, given that z(w) = 0.
-1, 0, 1
Let z(w) = -w**2 + 4*w + 5. Let j be z(4). Let a(k) = 4*k**2 + 2. Let s(r) = -9*r**2 + r - 5. Let g(y) = j*a(y) + 2*s(y). Factor g(o).
2*o*(o + 1)
Let f(n) be the second derivative of n**6/168 + n**5/35 - n**4/14 - n**3/2 - 6*n. Let x(q) be the second derivative of f(q). Factor x(h).
3*(h + 2)*(5*h - 2)/7
Let b(n) be the first derivative of n**6/120 + n**5/40 - n**3/3 - 2. Let p(x) be the third derivative of b(x). Factor p(j).
3*j*(j + 1)
Suppose 0*m - 2*m + 138 = 0. Find w, given that 24 - 7*w + 25*w + 18*w - 20*w**4 - m*w**3 + 2*w**4 - 54*w**2 = 0.
-2, -1/2, 2/3
Let o(a) = 2*a**2 - 8*a + 2. Let n be o(4). Determine i so that 1/2*i**4 + 2*i**3 + 1/2 + 2*i + 3*i**n = 0.
-1
Let p = -3/16 - -41/48. Let k(n) be the first derivative of -3 - 2*n**2 - 5/3*n**4 - p*n - 8/3*n**3 - 2/5*n**5. Suppose k(q) = 0. What is q?
-1, -1/3
Let o(v) be the first derivative of -4*v**3/3 + 8*v**2 - 16*v + 8. Factor o(x).
-4*(x - 2)**2
Let x(j) be the second derivative of j**5/90 + j**4/27 - 5*j**3/9 - 4*j**2 + 12*j + 1. Let x(u) = 0. Calculate u.
-3, 4
Let m be 3/2 + 2/4. Let z(o) be the first derivative of -o**4 - 1 - 2*o**3 + m*o + 1/2*o**2 + 4/5*o**5 + 1/2*o**6. Factor z(c).
(c - 1)*(c + 1)**3*(3*c - 2)
Let q(y) be the second derivative of 3*y**5/20 + 5*y**4/4 - 13*y**3/2 + 21*y**2/2 - 11*y - 3. Factor q(w).
3*(w - 1)**2*(w + 7)
Let f(z) be the second derivative of -z**8/10080 - z**7/1260 + z**5/45 - 5*z**4/12 + 2*z. Let p(j) be the third derivative of f(j). Factor p(s).
-2*(s - 1)*(s + 2)**2/3
Let g = -1663/9 + 185. Let m(q) be the third derivative of 3*q**2 - 1/18*q**4 - 1/60*q**5 + 1/180*q**6 + 1/630*q**7 + 0*q + g*q**3 + 0. Factor m(n).
(n - 1)**2*(n + 2)**2/3
Let i(c) be the third derivative of 0 + 0*c + 1/12*c**4 + 4/105*c**7 + 0*c**3 - 5*c**2 + 2/15*c**5 + 1/168*c**8 + 1/10*c**6. Factor i(s).
2*s*(s + 1)**4
Let g(c) be the first derivative of c**7/84 - c**6/60 - c**5/40 + c**4/24 - 5*c - 1. Let h(x) be the first derivative of g(x). Factor h(b).
b**2*(b - 1)**2*(b + 1)/2
Let f = 1059/4 + -264. Factor 1/4 - 1/2*y**3 - 1/4*y**5 + f*y - 3/4*y**4 + 1/2*y**2.
-(y - 1)*(y + 1)**4/4
Let p(h) be the first derivative of 5*h**3/3 + 5*h**2 + 5*h + 7. Factor p(g).
5*(g + 1)**2
Let r(t) be the first derivative of -t**5/5 - 5*t**4/16 + 7*t**3/12 + t**2/4 + 11. Factor r(g).
-g*(g - 1)*(g + 2)*(4*g + 1)/4
Let j(t) be the first derivative of -t**4/4 - 2*t**3/3 - t**2/2 + 8. Factor j(v).
-v*(v + 1)**2
Factor -h**2 + 1 + 2*h**2 - 5*h - 6*h**2 + 9.
-5*(h - 1)*(h + 2)
Let r(o) be the third derivative of -o**6/36 + 5*o**5/36 - 5*o**4/24 + 8*o**2. Factor r(k).
-5*k*(k - 1)*(2*k - 3)/3
Let f = -314/9 + 35. Let k(u) be the first derivative of -2/9*u - f*u**2 - 1 + 4/27*u**3. Suppose k(b) = 0. Calculate b.
-1/2, 1
Factor -8/5*v + 6/5*v**3 + 0 + 2/5*v**4 + 0*v**2.
2*v*(v - 1)*(v + 2)**2/5
Let d(h) be the second derivative of 0 + 1/9*h**3 + 1/126*h**7 - 1/20*h**5 - 1/36*h**4 + 4*h + 1/90*h**6 + 0*h**2. Factor d(k).
k*(k - 1)**2*(k + 1)*(k + 2)/3
Let w(y) be the third derivative of -y**5/30 + y**4/6 - y**3/3 - 8*y**2. Factor w(v).
-2*(v - 1)**2
Let n be (36/64)/(9/(-12)). Let m = n - -5/4. Factor 0 - 1/2*v**2 + 0*v - v**3 - m*v**4.
-v**2*(v + 1)**2/2
Let v(m) = -m**3 - 3*m**2 + m - 1. Let b(y) = -y**2 - 1. Let k(q) = -2*b(q) + v(q). Factor k(a).
-(a - 1)*(a + 1)**2
Let b(j) be the second derivative of 0 - j - 1/168*j**7 - 1/120*j**6 + 1/48*j**4 + 0*j**2 + 1/80*j**5 + 0*j**3. Factor b(y).
-y**2*(y - 1)*(y + 1)**2/4
Let a be ((-756)/(-30))/(2/(-11)). Let y = a + 139. Let -12/5*o**5 - 2/5*o + 0 + 14/5*o**3 - y*o**4 + 2/5*o**2 = 0. Calculate o.
-1, -1/2, 0, 1/3, 1
Factor 15*y + 0 - 5/2*y**2.
-5*y*(y - 6)/2
Suppose 41*r + 2*x - 4 = 38*r, -10 = -3*r + 4*x. Suppose 2/7 + 2/7*a**r + 4/7*a = 0. What is a?
-1
Let m(z) be the first derivative of z**6/1440 + z**3/3 - 3. Let c(x) be the third derivative of m(x). Factor c(i).
i**2/4
Determine z so that 2/7*z**2 - 4/7*z + 2/7 = 0.
1
Let c(u) be the first derivative of 0*u**2 + 2/15*u**5 + 3 + 0*u**3 + 0*u + 1/12*u**4 + 1/18*u**6. Find m such that c(m) = 0.
-1, 0
What is g in -2*g**2 - 2/3*g - 2*g**3 + 0 - 2/3*g**4 = 0?
-1, 0
Factor -79*d**2 + 17*d + 25*d**3 - 109*d**2 + 143*d**2 + 18*d - 10 - 5*d**4.
-5*(d - 2)*(d - 1)**3
Let y(w) be the second derivative of -w**5/15 + w**4/6 + 4*w**3/3 - w**2 - 2*w. Let k(i) be the first derivative of y(i). Factor k(s).
-4*(s - 2)*(s + 1)
Let z(q) = 10*q**2 + 11*q - 3. Le