Let w = d + 27. Factor 1/3*l**2 + w*l - 1/3.
(l - 1)*(l + 1)/3
Let y(b) be the first derivative of -3*b**4/8 + b**3/12 + 47. Factor y(l).
-l**2*(6*l - 1)/4
Let s(p) be the second derivative of p**7/10080 - 7*p**6/1440 + 49*p**5/480 + p**4/6 + 4*p**3 - 51*p. Let l(t) be the third derivative of s(t). Factor l(y).
(y - 7)**2/4
Let o(r) be the third derivative of 0*r**3 + 0 + 1/240*r**6 - 1/48*r**4 + 0*r**5 + 0*r + 39*r**2. Let o(a) = 0. What is a?
-1, 0, 1
Let w(t) be the third derivative of t**6/30 - 8*t**4 + 256*t**3/3 - 4*t**2 - 11. Let w(f) = 0. What is f?
-8, 4
Factor -1957*j + 430*j**2 + 12 - 6*j**3 - 12 + j**3 - 7288*j.
-5*j*(j - 43)**2
Let b(a) be the second derivative of -a**5/110 + 9*a**4/22 - 17*a**3/11 + 25*a**2/11 - 61*a. Factor b(c).
-2*(c - 25)*(c - 1)**2/11
Let x be -5 + 4 + 1 + 1. Let s be (15/(-6) + x)*8/(-6). What is c in -94/3*c**3 - 16/3*c**4 + 32/3*c**5 + 26/3*c - 16/3*c**s - 4/3 = 0?
-1, 1/4, 2
Let f(g) = 2*g**3 - 32*g**2 + 61*g + 75. Let m(p) = -4*p**3 + 48*p**2 - 92*p - 112. Let v(n) = 8*f(n) + 5*m(n). Suppose v(s) = 0. Calculate s.
-5, -1, 2
Let p = 5 - 11. Let a be p/(-3) + (-3 - -4). Factor 4/3*m**2 - 1/3*m**a + 0 - m.
-m*(m - 3)*(m - 1)/3
Suppose -2*c + 2*o = -8, -20 = c - 3*o + 8*o. Let w(r) be the first derivative of -9 + 1/15*r**3 + c*r + 0*r**2. Solve w(l) = 0 for l.
0
Let w(g) be the first derivative of -g**4/4 + 151*g**3/3 - 5775*g**2/2 + 5625*g - 392. Factor w(c).
-(c - 75)**2*(c - 1)
Let x be -2 - 284/(-120) - (-7 + 144/20). Let x*v**4 - 1/6 + 0*v**2 - 1/3*v**3 + 1/3*v = 0. What is v?
-1, 1
Let o(l) = 3*l**2 - 6*l + 3. Let t(v) = -v**2 + v - 1. Suppose -2*g - 11 = -1. Let d(y) = g*o(y) - 20*t(y). Find m such that d(m) = 0.
-1
Let h(p) be the second derivative of p**5/30 - p**4/3 + p**3 - 9*p**2/2 + 6*p. Let v(g) be the first derivative of h(g). Factor v(s).
2*(s - 3)*(s - 1)
Let r(k) be the second derivative of 1/30*k**5 + 1/135*k**6 + 5*k - 1/27*k**4 + 0 - 8/9*k**2 - 4/9*k**3. Factor r(z).
2*(z - 2)*(z + 1)*(z + 2)**2/9
Let q(f) be the third derivative of -1/20*f**5 + 7*f**2 + 0*f + 1/2*f**4 + 0 - 3/2*f**3. Factor q(k).
-3*(k - 3)*(k - 1)
Let c(n) be the first derivative of n**3/21 - 118*n**2/7 + 235*n/7 + 453. Factor c(t).
(t - 235)*(t - 1)/7
Let i(n) = 37*n - 5. Let j be i(2). Determine r so that j*r - 70*r - 2*r**2 + 3*r**2 = 0.
0, 1
Let q(n) be the first derivative of 2*n**5/5 - 17*n**4 + 280*n**3 - 2200*n**2 + 8000*n - 89. Factor q(g).
2*(g - 10)**3*(g - 4)
Let f = 40874/981 - -1/981. Let k = -41 + f. What is l in 0 + k*l**2 + 2/3*l = 0?
-1, 0
Let c be 33/(-99) + 14/6. Factor -1/2*x**c + 1/2*x + 0.
-x*(x - 1)/2
Let j(y) be the first derivative of -11 + 5/3*y**3 + y**5 + 80*y - 15/2*y**4 + 60*y**2. Suppose j(d) = 0. What is d?
-1, 4
Let k be (-411)/(-630) - 180/(-840) - (-2)/(-10). Factor -5/3*i**2 + 1/2 - k*i**3 + 2/3*i + 7/6*i**4.
(i - 1)**2*(i + 1)*(7*i + 3)/6
Let o(y) be the first derivative of 0*y - 2/3*y**3 - 1/6*y**4 - 1/9*y**6 - 1 + 2/5*y**5 + 2/3*y**2. Let o(g) = 0. What is g?
-1, 0, 1, 2
Let g(c) = c**3 + c - 1. Suppose 0 = -v - 3*v - 8, -2*v - 12 = -k. Let j(d) = -22*d**3 + 46*d**2 - 48*d + 16. Let f(o) = k*g(o) + j(o). What is h in f(h) = 0?
2/7, 1, 2
Let k(b) be the second derivative of 5/4*b**4 + 0*b**3 + 1/4*b**5 + 0 + 0*b**2 - 36*b. Factor k(u).
5*u**2*(u + 3)
Suppose 9/4*k**3 - 81/4*k + 27/8 + 30*k**2 - 27/8*k**4 = 0. What is k?
-3, 1/3, 3
Let b(g) = -11*g**2 - g**3 + 41*g - 78*g + 28 + 51*g. Let h be b(-12). Factor 2/5*u + 0 + 2/5*u**h - 2/5*u**3 - 2/5*u**2.
2*u*(u - 1)**2*(u + 1)/5
Factor 48/7*x**2 - 768/7 + 36/7*x**3 - 320/7*x + 4/7*x**4.
4*(x - 3)*(x + 4)**3/7
Let p(o) be the first derivative of -o**6/6 + o**5/10 + 3*o**4/2 - 11*o**3/3 + 7*o**2/2 - 3*o/2 + 71. Let p(c) = 0. Calculate c.
-3, 1/2, 1
Let f(z) be the first derivative of -2/9*z**2 - 2/9*z**3 + 31 + 0*z - 1/18*z**4. Factor f(p).
-2*p*(p + 1)*(p + 2)/9
Suppose 7*d - 13 - 1 = 0. Find s such that 0*s**2 - 7*s**3 + 6*s**3 + s - d*s**2 + 2 = 0.
-2, -1, 1
Let l be (-5)/6*(864/60 - 15). Factor 0 - l*j**2 - j.
-j*(j + 2)/2
Let v(y) = -y**2 + 58*y - 52. Let k be v(57). Let t(r) be the first derivative of -1/5*r**k - 4*r - 13/3*r**3 - 6*r**2 - 3/2*r**4 - 11. Factor t(a).
-(a + 1)**2*(a + 2)**2
Let o = -11573/4 + 2894. Factor 3/8*z**3 + 3/2 - 21/8*z + o*z**2.
3*(z - 1)**2*(z + 4)/8
Let b be -12*(12/(-8) - -1) + -2. Suppose -b*c + c = -6. What is l in -c*l**2 - 4/3*l + 10/3*l**3 + 0 = 0?
-2/5, 0, 1
Let s(y) = -y**3 + 5*y**2 - 3*y + 1. Let z be s(4). Factor 12*b**2 - 63*b**4 + 29*b**4 + 28*b**4 - 6 + 2*b**3 - b - b**z.
-(b - 1)**2*(b + 1)**2*(b + 6)
Suppose -2*v + 8*v = -558. Let n = 281/3 + v. Solve -n*p + 1/3*p**2 + 0 = 0.
0, 2
Let h(z) be the first derivative of z**4/36 + z**3/9 - z**2/2 + 2*z + 10. Let s(y) be the first derivative of h(y). Determine a so that s(a) = 0.
-3, 1
Let c(n) be the first derivative of -n**3/15 + 7*n**2/2 - 261. What is y in c(y) = 0?
0, 35
Suppose 3/2 + 9*z**2 - 6*z**3 + 3/2*z**4 - 6*z = 0. Calculate z.
1
Let h(c) be the third derivative of c**7/840 - 29*c**6/480 + 27*c**5/80 - 79*c**4/96 + 13*c**3/12 - 29*c**2 - 2*c. Factor h(f).
(f - 26)*(f - 1)**3/4
Let f(g) be the second derivative of g**7/378 + g**6/54 + g**5/30 - g**4/27 - 4*g**3/27 + 451*g. Factor f(q).
q*(q - 1)*(q + 2)**3/9
Let l(b) be the third derivative of b**5/60 - 5*b**4/24 - b**3 - 52*b**2 + b. Factor l(i).
(i - 6)*(i + 1)
Let q(x) = 2*x - 7. Let j be q(-7). Let l = j + 23. Determine h so that -2*h - 2*h**l - 1 - 3 + 4 = 0.
-1, 0
Let r be 35/(-4) + -1 - (-3)/4. Let q be 3/r + 33/45. Factor -q + 0*o + 0*o**3 + 4/5*o**2 - 2/5*o**4.
-2*(o - 1)**2*(o + 1)**2/5
Factor -17*i - 8*i**4 - 127*i**3 - 5 + 249*i**3 + 1 - i**5 - 144*i**3 - 28*i**2.
-(i + 1)**4*(i + 4)
Let f = -73 - -112. Let d be 306/f + (-4)/(-26). What is i in 2*i**3 + 0*i + 19*i**2 - d + 0*i - 13*i**2 = 0?
-2, 1
Let o(v) = -v - 4. Let t be o(-6). Let d = 1567/14 - 689/7. What is c in -d*c + 3 + 6*c**t = 0?
1/4, 2
Suppose 7 = 4*n + 3. Let f be ((21 - n) + -8)*4/18. Let -f*m + 0 - 2/3*m**2 = 0. What is m?
-4, 0
Let s(a) = a**3 - 9*a**2 - 9*a - 6. Let q be s(10). Factor q*j**2 + 48 + 16*j - 19 - 17.
4*(j + 1)*(j + 3)
Find h, given that 1/2*h - 1/6*h**3 + 1/3 + 0*h**2 = 0.
-1, 2
Let w(n) be the first derivative of 4*n**3/3 + 214*n**2 - 26. Let w(z) = 0. Calculate z.
-107, 0
Suppose 37 = -6*o + 49. Solve 20 + 253*x + 5*x**o + 265*x - 538*x = 0.
2
Let d = 9 - 3. Suppose 4*t = -3*c + d, -6 = -5*c + 2*c - 3*t. What is z in -4/3*z**c - 2/9 + 8/9*z - 2/9*z**4 + 8/9*z**3 = 0?
1
Let l(s) = -5*s**4 + 19*s**3 - 28*s**2 - 13*s + 24. Let i(t) = -4*t**4 + 18*t**3 - 28*t**2 - 14*t + 26. Let c(j) = 6*i(j) - 4*l(j). Find d, given that c(d) = 0.
-1, 1, 3, 5
Let d(i) be the first derivative of 0*i - 3/4*i**4 - 27 - 2*i**2 + 2/5*i**5 - 8/3*i**3 + 1/6*i**6. Factor d(c).
c*(c - 2)*(c + 1)**2*(c + 2)
Suppose 9 + 5 = 7*y. Find n such that 2*n - 6*n**2 + 5*n - 2*n + n**y = 0.
0, 1
Solve 2/3*n**3 - 52/3*n**2 - 18*n + 0 = 0 for n.
-1, 0, 27
Solve -37*u**2 + 16*u**2 + 20*u**2 - 15 + 16*u = 0 for u.
1, 15
Let u(m) be the second derivative of -m**5/10 + 20*m**4/3 - 400*m**3/3 - 37*m. Determine s, given that u(s) = 0.
0, 20
Let m(s) be the first derivative of s**6/30 - s**5/10 - 32*s + 32. Let w(a) be the first derivative of m(a). Find k such that w(k) = 0.
0, 2
Let t(z) be the third derivative of -25*z**8/336 + z**7/42 + 5*z**6/24 - z**5/12 - 4*z**2 - 9*z. Determine s so that t(s) = 0.
-1, 0, 1/5, 1
Let y be 2/(-40)*2*(-30)/72. Let i(l) be the second derivative of -y*l**4 + 1/2*l**2 + 0 + 6*l - 1/12*l**3. Factor i(m).
-(m - 1)*(m + 2)/2
Determine v, given that 7/4*v - 1/4*v**5 + 3/4 - 5/4*v**4 + 1/2*v**2 - 3/2*v**3 = 0.
-3, -1, 1
What is o in o**5 - 3*o**5 - o**3 + 3*o**3 - 4*o**2 - 1503 + 1503 + 4*o**4 = 0?
-1, 0, 1, 2
Let r(f) be the third derivative of 1/45*f**4 + 0*f + 2/225*f**5 + 0 - f**2 + 0*f**3 + 1/900*f**6. Factor r(w).
2*w*(w + 2)**2/15
Solve -1/8*m**2 + 0 - 2*m = 0.
-16, 0
Suppose 3*d + 0*d = 0. Suppose d = -6*t + 5*t + 3. Determine q so that 2/3 + 2/3*q**t + 2*q + 2*q**2 = 0.
-1
Let v(w) = 3*w**2 - w - 1. Let f(g) = 23*g**2 + 29*g - 96. Let y(z) = f(z) - 6*v(z). Factor y(p).
5*(p - 2)*(p + 9)
Let o(s) = -3*s**3 - 5*s**2 - 2*s. Let z(d) = -d**2 - d. Let r(u) = -u + 10. Let i be r(7). Suppose -5 = -2*c