81*d - 6851. Let o(r) = -7*r**3 + 355*r**2 + 6485*r + 41102. Let a(h) = 6*o(h) + 39*u(h). Solve a(f) = 0.
-19
Let q(h) be the second derivative of 1/15*h**6 + 2/5*h**5 - 4*h - 4/3*h**3 + 1/2*h**4 - 4*h**2 + 0. Factor q(p).
2*(p - 1)*(p + 1)*(p + 2)**2
Let c(p) be the third derivative of -p**5/120 + 7*p**4/48 + 2*p**3/3 + 2*p**2 + 7. Factor c(j).
-(j - 8)*(j + 1)/2
Factor 133 - 248 + 70*t**2 + 140 - 95*t.
5*(t - 1)*(14*t - 5)
Let f(r) be the third derivative of r**6/180 + r**5/30 - r**4/36 - r**3/3 + 54*r**2. Factor f(g).
2*(g - 1)*(g + 1)*(g + 3)/3
Let z(t) = 2*t**2 + 3. Let g(i) = -i**2 - i + 1. Suppose 4*s + 3 = 3*x, 2*x - 2*s + 21 = 5*x. Let p(n) = x*g(n) - z(n). Solve p(b) = 0.
-1, 2/7
Suppose -7 - 154*r**3 - 677*r**3 - 168*r - 15*r**5 + 309*r**4 - 363*r**3 - 377 + 1452*r**2 = 0. Calculate r.
-2/5, 1, 2, 16
Let q = 1914 + -1913. Let u(a) be the first derivative of -6*a**2 + 4/3*a**3 - q + 0*a. Factor u(d).
4*d*(d - 3)
Let d(v) = 5*v**4 + 30*v**3 + 45*v**2 - 30*v - 45. Let q(h) = -5*h**4 - 30*h**3 - 44*h**2 + 30*h + 45. Let b(y) = -4*d(y) - 5*q(y). Suppose b(c) = 0. What is c?
-3, -1, 1
Let k be ((-15)/9)/(130/(-156)). Let b(q) be the third derivative of 0*q**3 - 1/130*q**5 + 0*q + 0*q**4 + 1/195*q**6 - 1/1365*q**7 - 11*q**k + 0. Factor b(g).
-2*g**2*(g - 3)*(g - 1)/13
Let o be 36/(-63)*(-3 + 1). Let k be (46/(-6) + 6)/(15/(-18)). Let 4/7*g**k + 8/7*g**3 - o*g + 2/7 - 6/7*g**4 = 0. What is g?
-1, 1/3, 1
Let c(o) = 5184*o**4 + 4891*o**3 + 1732*o**2 + 267*o + 16. Let r be 1/(2 - (-3 - -6)). Let n(y) = y**3 + y. Let w(m) = r*c(m) - 5*n(m). Factor w(h).
-4*(4*h + 1)**2*(9*h + 2)**2
Find j, given that -12/5*j**3 - 26/5*j**4 + 0*j**2 + 0 - 4/5*j**5 + 0*j = 0.
-6, -1/2, 0
Let s(g) be the second derivative of -g**8/10080 - g**7/2520 - g**6/2160 - g**3/6 - 14*g. Let n(v) be the second derivative of s(v). Factor n(r).
-r**2*(r + 1)**2/6
Suppose -98*b = -50*b - 96. Suppose 2/11*r**b + 10/11*r**3 + 0*r + 14/11*r**4 + 0 + 6/11*r**5 = 0. Calculate r.
-1, -1/3, 0
Let a(u) be the third derivative of -u**6/40 + u**5/5 - u**4/8 - 3*u**3 - 31*u**2 + 2. Determine n, given that a(n) = 0.
-1, 2, 3
Let c(s) be the third derivative of -4*s**2 + 0*s - 1/60*s**6 + 0 + 1/6*s**3 + 1/210*s**7 - 1/30*s**5 + 1/24*s**4 + 1/336*s**8. Factor c(l).
(l - 1)**2*(l + 1)**3
Suppose 3*h + 56 = 7*h + 4*z, 0 = -5*z. Suppose -8*p + 2 = -h. Factor -18/11*m - 4/11 - 8/11*m**p.
-2*(m + 2)*(4*m + 1)/11
Suppose 4*k - 7*k - 434 = -4*w, -10 = 5*k. Let r = 429/4 - w. Factor 0*q - r*q**3 + 1/2*q**2 + 0.
-q**2*(q - 2)/4
Let v(m) be the third derivative of m**5/5 + 10*m**4/3 + 8*m**3 - 62*m**2. Factor v(s).
4*(s + 6)*(3*s + 2)
Let z(g) be the third derivative of -g**7/7980 - g**6/1140 - g**5/570 - 5*g**3/6 - 21*g**2. Let m(k) be the first derivative of z(k). Factor m(x).
-2*x*(x + 1)*(x + 2)/19
Let d(q) be the third derivative of -q**8/84 - 4*q**7/105 + 2*q**5/15 + q**4/6 - 298*q**2. Factor d(r).
-4*r*(r - 1)*(r + 1)**3
Let w(f) = 2*f**4 + 14*f**3 - 72*f**2 + 14*f + 96. Let a(t) = -5*t**4 - 43*t**3 + 216*t**2 - 41*t - 288. Let v(q) = -2*a(q) - 7*w(q). Factor v(u).
-4*(u - 2)**2*(u + 1)*(u + 6)
Let g(c) be the first derivative of -9*c**4/2 - 14*c**3 + 17*c**2 - 6*c - 17. Factor g(n).
-2*(n + 3)*(3*n - 1)**2
Let a = 1908 - 11447/6. Suppose 0*g**2 + 1/3*g**3 - 1/6 - 1/3*g + a*g**4 = 0. Calculate g.
-1, 1
Let y be 5*(7 + -3) + -4. Let w = y + -16. Find d, given that w*d + 5*d + 0*d - 10*d**3 + 5*d - 5 + 5*d**4 = 0.
-1, 1
Let l(r) = 4*r + 10. Let a be l(4). Let m be (3 - 13/4)*(-16)/a. Find t such that 2/13*t**3 - 4/13*t + 0 - m*t**2 = 0.
-1, 0, 2
Find k such that 0 - 312/7*k**2 + 44*k + 4/7*k**3 = 0.
0, 1, 77
Suppose -2*t = 2*t + 16. Let w(m) = -m**2 - 4*m + 3. Let c be w(t). Factor -6*i**2 + 2 - 2*i + 4*i**2 + i**3 + i**c.
2*(i - 1)**2*(i + 1)
Let g = 22 + -20. Find x, given that x**2 - 2*x + 4*x**3 - 7*x**g + 8*x**2 = 0.
-1, 0, 1/2
Let b be (-3)/5 + (-432)/80. Let t(p) = 13*p**3 - 22*p**2 + 70*p - 61. Let w(k) = 7*k**3 - 11*k**2 + 35*k - 31. Let y(g) = b*t(g) + 11*w(g). Factor y(a).
-(a - 5)**2*(a - 1)
Let o = -304/4935 + 2/105. Let x = 198/235 + o. What is l in 16/5*l**4 - 16/5*l + 0 + x*l**5 - 16/5*l**2 + 12/5*l**3 = 0?
-2, -1, 0, 1
Let f = -11 - -16. Let b = -3 + f. Factor 2*d - 5*d**3 + d**3 + b*d**5 - 3*d**5 + 3*d**5.
2*d*(d - 1)**2*(d + 1)**2
Factor 3/8*i + 0 + 7/8*i**2 + 1/8*i**4 + 5/8*i**3.
i*(i + 1)**2*(i + 3)/8
Let o(i) be the third derivative of -i**7/420 - i**6/30 - i**5/10 + 2*i**4/3 + 16*i**3/3 + 211*i**2 - i. Let o(t) = 0. What is t?
-4, -2, 2
Let c be (-1)/(-2 - (-7 + 2)*18/60). Find q, given that 32/13*q + 128/13 + 2/13*q**c = 0.
-8
Let b = 51 + -49. Find l, given that -15*l**4 - 4*l**2 + l**b - 2*l**2 + 5*l**5 + 15*l**3 = 0.
0, 1
Let v be (25/75)/(14/12 + -1). Factor -v*k**2 + 2/3*k**3 + 0 + 4/3*k.
2*k*(k - 2)*(k - 1)/3
Let r(n) = 535*n**2 + 1 - 531*n**2 + 3*n + 2 + 4*n**3. Let t(u) = 4*u**3 + 4*u**2 + 4*u + 4. Let c(z) = 4*r(z) - 3*t(z). Factor c(f).
4*f**2*(f + 1)
Suppose 0*a + 5*d - 31 = 2*a, -52 = 5*a - 4*d. Let i be 4/(-9)*(-12)/a + 2. Factor i*l**2 + 0 - 2/3*l.
2*l*(2*l - 1)/3
Suppose -4 = h - 14. Factor -53 - h*r - 18*r**3 - 12*r**2 + 50 + 15*r**4 + 28*r.
3*(r - 1)**2*(r + 1)*(5*r - 1)
Let y be 8/56 - ((-164)/(-14))/(-2). Let v(g) be the third derivative of 0*g + 0*g**3 + 0 + 1/30*g**y + 8*g**2 + 1/3*g**4 - 1/5*g**5. Let v(a) = 0. Calculate a.
0, 1, 2
Let x(r) be the second derivative of 1/48*r**4 + 0*r**3 - 1/2*r**2 - 30*r + 0. Factor x(k).
(k - 2)*(k + 2)/4
Suppose -4*d - 97*z + 30 = -102*z, 3*z = -18. Determine k so that 0*k + d*k**3 + 1/6*k**2 + 0 - 1/6*k**4 = 0.
-1, 0, 1
Suppose 2*i - 3 = 2*f + 7, -i = 3*f - 1. Factor -1/2*x**3 - 3/2*x**2 + 1/2*x**i + 1/2*x + 1.
(x - 2)*(x - 1)*(x + 1)**2/2
Let m(o) be the first derivative of o**6/2 - 3*o**5/2 - 33*o**4/4 - 15*o**3/2 + 706. Determine d so that m(d) = 0.
-3/2, -1, 0, 5
Let c(n) = -4*n - 3. Let u be c(-3). Factor 4*g**2 - u*g**2 - 2*g + 9*g**2 - 6*g.
4*g*(g - 2)
Let z = 42 - 30. Suppose -2*r**2 - 20*r**3 + 18*r**2 + 20*r**4 - 4*r - z*r**4 = 0. What is r?
0, 1/2, 1
Let g = -2875 - -2878. Suppose -3/4*m + 0*m**4 - 1/2*m**2 + m**g + 1/2 - 1/4*m**5 = 0. Calculate m.
-2, -1, 1
Let t be 1160/(-800) + (-6)/(-4). Let w(f) be the third derivative of 2*f**2 - t*f**5 + 1/16*f**4 + 0*f**3 + 0*f + 1/80*f**6 + 0. Factor w(j).
3*j*(j - 1)**2/2
Let y = 27 - 28. Let l(c) = 20*c**2 - 7*c - 2. Let f(x) = -x - 1. Let t(v) = y*l(v) + 2*f(v). Factor t(g).
-5*g*(4*g - 1)
Let j(s) be the second derivative of -s**6/12 - s**5/8 + 342*s. Factor j(n).
-5*n**3*(n + 1)/2
Suppose -1936/9 + 704/3*d - 20*d**2 + 4/9*d**3 = 0. What is d?
1, 22
Suppose w + 3*y = 13, 0 = -9*y + 4*y + 15. Factor 4*z**3 + 0*z - w*z + 0*z.
4*z*(z - 1)*(z + 1)
Let t(k) be the first derivative of -3/40*k**5 + 3/16*k**4 - 3/8*k**2 + 0*k + 1/8*k**3 - 20. Suppose t(x) = 0. What is x?
-1, 0, 1, 2
Let z(k) = 2*k**3 - 4*k**2 - 6*k. Let t be 2 - ((0 - -1)/1)/(-1). Let w(i) = i**3 - 5*i**2 - 7*i - 1. Let u(a) = t*z(a) - 4*w(a). Factor u(c).
2*(c + 1)**2*(c + 2)
Let i be ((-6)/(-16))/(11 + -5). Let z(t) be the first derivative of -1/20*t**5 - 1/8*t**2 + i*t**4 + 1/12*t**3 + 8 + 0*t. Factor z(n).
-n*(n - 1)**2*(n + 1)/4
Let a = 20 - 39/2. Let c(v) be the third derivative of 3*v**2 + 0 + a*v**3 + 1/40*v**6 + 0*v - 1/20*v**5 - 1/8*v**4. Factor c(b).
3*(b - 1)**2*(b + 1)
Let o(t) be the second derivative of -t**5/60 - t**4/12 + t**3/18 + t**2/2 - 24*t. Factor o(l).
-(l - 1)*(l + 1)*(l + 3)/3
Factor 18 - 1/5*f**3 + 16/5*f**2 - 69/5*f.
-(f - 10)*(f - 3)**2/5
Let d(z) = -30*z - 19. Let x be d(-3). Let l = 73 - x. Determine j, given that -1/2*j**4 + 0 + 1/2*j**l + 1/4*j - 1/4*j**5 + 0*j**3 = 0.
-1, 0, 1
Suppose 2*z + 5*b = 3, -b = z - 2 - 4. Let q = z - 6. Let 0*f - 11*f - f + 18 - 3*f + q*f**2 = 0. Calculate f.
2, 3
Let f(w) be the third derivative of -w**5/240 + 5*w**4/24 + 7*w**3/8 - 320*w**2. Suppose f(y) = 0. Calculate y.
-1, 21
Suppose 23*r - 16*r = 0. Let o(k) be the third derivative of -17/144*k**4 + r*k + 2*k**2 - 7/120*k**5 + 0 + 1/80*k**6 - 1/12*k**3. Determine d so that o(d) = 0.
-1/3, 3
Let w(s) be the third derivative of s**8/26880 - s**7/1440 - s**6/2880 + 7*s**5/480 + s**4/8 + 39*s**2. Let a(g) be the second derivative of w(g). Factor a(c).
(c - 7)*(c - 1)*(c + 1)/4
Let o