 be the first derivative of c**4/4 + 7*c**3/3 + 5*c**2 - 150. Factor d(h).
h*(h + 2)*(h + 5)
Let q = 1161 + -1161. Let t(p) be the third derivative of 0*p**3 + 1/180*p**6 + q + 0*p**4 + 0*p**5 + p**2 + 0*p + 1/315*p**7. Let t(b) = 0. What is b?
-1, 0
Let n(u) be the third derivative of -1/6*u**4 - 1/6*u**3 + 0*u + 2*u**2 - 7/240*u**5 + 0. Factor n(x).
-(x + 2)*(7*x + 2)/4
Let n = 2454 - 73619/30. Let g(v) be the third derivative of 0*v**3 + 0*v + 0 - 13*v**2 + 0*v**4 - n*v**5. Suppose g(x) = 0. What is x?
0
Suppose 0*f = 4*f - 12. Suppose -2*o - f*o + c = -14, 5*o + 4*c - 19 = 0. Factor o*r**2 + r**3 - 8*r - r**2 + 9*r.
r*(r + 1)**2
Let u(x) be the first derivative of -3*x**6/13 + 66*x**5/65 + 5*x**4/2 - 2*x**3/3 - 56*x**2/13 - 40*x/13 + 152. Find h such that u(h) = 0.
-1, -2/3, 1, 5
Let i(q) be the first derivative of -2*q**4 - 4*q**3 + 8*q**2 - 15 + 16*q + 4/5*q**5. Factor i(v).
4*(v - 2)**2*(v + 1)**2
Let v(t) be the first derivative of -4/9*t**3 + 1/15*t**5 + 2 + 1/9*t**4 + 4*t + 0*t**2. Let l(s) be the first derivative of v(s). Find g, given that l(g) = 0.
-2, 0, 1
Factor 0 - 4/15*l**3 - 2/15*l - 2/5*l**2.
-2*l*(l + 1)*(2*l + 1)/15
Let p = 82/43 - 121/86. Determine f so that 1/4*f**5 + 1/4*f**4 + 1/4*f - 1/2*f**2 - p*f**3 + 1/4 = 0.
-1, 1
Let x(z) be the second derivative of 5/42*z**7 - 5*z**2 + 7/2*z**5 + 12*z + 0 - z**6 + 15/2*z**3 - 20/3*z**4. Let x(q) = 0. Calculate q.
1, 2
Let k be (-1 - 1/(-3))/(2/(-9)). Determine i so that 8*i**k - 4*i**5 + 4*i**4 - 47*i**2 + 47*i**2 = 0.
-1, 0, 2
Factor -18*k - 10 + 27 + 1283*k**2 - 1282*k**2.
(k - 17)*(k - 1)
Let k(c) = c**2 - 10*c - 14. Let s(f) be the third derivative of 0*f - 1/24*f**4 + 1/6*f**3 - 3*f**2 + 0 + 1/60*f**5. Let j(x) = -3*k(x) + 6*s(x). Factor j(m).
3*(m + 4)**2
Let h(r) be the third derivative of r**6/420 + 2*r**5/105 + r**4/21 - 13*r**2 - r. Find v, given that h(v) = 0.
-2, 0
Find i such that 0 - 100/3*i - 5/3*i**4 - 5/3*i**3 + 80/3*i**2 = 0.
-5, 0, 2
Let v(t) be the first derivative of t**4 + 2*t**3/3 - t**2 + 117. Let v(i) = 0. What is i?
-1, 0, 1/2
Let r(f) be the third derivative of 0 - 42*f**2 + 1/5*f**5 + 1/20*f**6 + 0*f + 5/12*f**4 + 1/2*f**3 + 1/210*f**7. Factor r(g).
(g + 1)**3*(g + 3)
Let u(y) be the first derivative of 1/36*y**4 - 3/2*y**2 + 1/45*y**5 + 4 + 0*y + 0*y**3 + 1/180*y**6. Let z(d) be the second derivative of u(d). Factor z(t).
2*t*(t + 1)**2/3
Suppose 3*m + 58 = -2*a, 40 = -a - 4*m + 6. Let u = a + 31. Factor 2*g**3 - 2/3*g**u - 8/3*g**2 + 4/3*g**4 - 8/3*g + 0.
-2*g*(g - 2)**2*(g + 1)**2/3
Suppose -24*n**4 + 48/7*n**5 + 21*n**3 - 33/7*n - 6/7 + 12/7*n**2 = 0. Calculate n.
-1/4, 1, 2
Let z(m) be the first derivative of -m**3/3 + 14*m**2 + 29*m - 34. Suppose z(k) = 0. What is k?
-1, 29
Let a(u) be the third derivative of -u**6/300 - 3*u**5/25 - 11*u**4/20 - 16*u**3/15 + 31*u**2 + 2. Factor a(h).
-2*(h + 1)**2*(h + 16)/5
Let h(s) = 2*s - 3. Let i be h(4). Determine j so that 43*j**4 + 2*j**3 - 49*j**4 + 6*j**2 - 2*j**3 + 3*j**i - 3*j = 0.
-1, 0, 1
Let p(k) be the third derivative of 0*k + 1/140*k**5 - 28*k**2 + 0 + 3/7*k**3 + 1/8*k**4. Factor p(u).
3*(u + 1)*(u + 6)/7
Let o(c) = -c**2 + 2*c + 2. Let r be o(0). Factor 769 - 775 - 5*l + r*l**2 + l.
2*(l - 3)*(l + 1)
Let o(y) be the second derivative of -y**8/336 + 2*y**7/105 - y**6/30 + 5*y**2/2 + 13*y. Let p(i) be the first derivative of o(i). Factor p(l).
-l**3*(l - 2)**2
Let b = -5 + 19/3. Let h be (4/11)/2 + 40/(-220). What is a in 2/3*a**4 + b*a + 10/3*a**2 + h + 8/3*a**3 = 0?
-2, -1, 0
Let d(s) be the second derivative of 0 + 1/6*s**4 + 1/30*s**5 + 4*s + 5/3*s**2 - s**3. Factor d(u).
2*(u - 1)**2*(u + 5)/3
Let g = -2/265 + 536/795. Suppose -2/3*d**4 + 0*d + g*d**2 + 0 + 0*d**3 = 0. Calculate d.
-1, 0, 1
Let q = -11 - 6. Let i = 19 + q. Solve 9 - y**i + 0*y**2 - 15*y + 7*y**2 = 0.
1, 3/2
Let x(q) = -q**2 - 25*q - 28. Let t be x(-18). Factor -4*i**2 + 52*i - t*i + 50*i.
-4*i*(i - 1)
Let z(f) be the first derivative of -f**4/2 - 38*f**3/3 - 112*f**2 - 384*f + 213. Factor z(h).
-2*(h + 3)*(h + 8)**2
Determine n, given that 0 - 1/2*n**5 - 17/10*n**3 + 0*n**2 + 2/5*n + 9/5*n**4 = 0.
-2/5, 0, 1, 2
Let f(r) be the second derivative of r**7/42 - r**6/24 - r**5/12 + 5*r**4/24 + r**2 + 4*r. Let c(d) be the first derivative of f(d). Factor c(q).
5*q*(q - 1)**2*(q + 1)
Let c(t) be the second derivative of 21*t + 0 + 1/22*t**4 + 1/11*t**3 + 1/11*t**2 + 1/110*t**5. Let c(z) = 0. Calculate z.
-1
Solve -278 - 2*d + 3527 + 4*d**2 - 15*d**2 + 12*d**2 + 116*d = 0 for d.
-57
Let j(w) be the second derivative of -w**6/660 + w**5/660 - 5*w**3/6 - 16*w. Let o(r) be the second derivative of j(r). Factor o(z).
-2*z*(3*z - 1)/11
Let j(u) be the first derivative of 24*u**2 + 20 + 2/5*u**5 + 44/3*u**3 + 18*u + 4*u**4. Factor j(c).
2*(c + 1)**2*(c + 3)**2
Let u(g) be the second derivative of 1/3*g**6 + 0 - 16/7*g**2 - 68/21*g**4 - 32/7*g**3 + 12/35*g**5 - 7*g. What is d in u(d) = 0?
-2, -2/5, -2/7, 2
Factor -1/3*j**4 - 32/3 + 4*j**2 + 8/3*j - 2/3*j**3.
-(j - 2)**2*(j + 2)*(j + 4)/3
Let y(w) be the second derivative of 3*w**5/20 + 31*w**4/4 + 112*w**3 - 384*w**2 - 627*w. Suppose y(j) = 0. Calculate j.
-16, 1
Let z be (-2425)/(-17000) - (-4)/(-34). Let d(k) be the third derivative of -1/2*k**3 + 0 + 5*k**2 + 0*k + 1/16*k**4 + z*k**5. Solve d(w) = 0 for w.
-2, 1
Let w(b) be the third derivative of b**6/60 - b**5/30 - 2*b**4/3 + 4*b**3 - 215*b**2. Let w(k) = 0. What is k?
-3, 2
Let x be (-301)/(-210) - 1 - (3 + 0)/30. What is t in -25/3 - x*t**2 + 10/3*t = 0?
5
Let d(v) be the first derivative of -2*v**3/39 - 68*v**2/13 - 2312*v/13 - 183. Factor d(w).
-2*(w + 34)**2/13
Let k(m) = -1225*m**2 - m + 0*m - 3 + 1229*m**2. Let p(i) = -i - 7*i**2 + 5 + 3*i - i. Let x(g) = -10*k(g) - 6*p(g). Factor x(q).
2*q*(q + 2)
Let b(m) be the first derivative of -m**6/3 + 14*m**5/5 - 7*m**4 + 16*m**3/3 - 3. Solve b(z) = 0 for z.
0, 1, 2, 4
Suppose -244/5*n + 7442/5*n**2 + 2/5 = 0. Calculate n.
1/61
Suppose 10 = 7*l - 11. Suppose 14*o**4 - 92*o**2 - 100*o**l + 8 + 8*o**2 - 50*o**4 - 12*o = 0. What is o?
-1, 2/9
Let k be 1 + 3 + (-2)/(-2). Suppose -k*i + 5*f + 10 = 0, -4 = -4*i - i + 2*f. Let 4*b**2 + i - 3 - 1 + 4*b**3 - 4*b = 0. Calculate b.
-1, 1
Suppose 3*t = 2 + 7. Factor 3*k**3 + 2*k**2 + 0*k**2 - 2*k**t.
k**2*(k + 2)
Suppose 10*d + 6 + 75*d**3 + 15*d - 21 - 80*d**3 - 5*d**2 = 0. Calculate d.
-3, 1
Suppose 0 = -3*i + 5*z + 15 + 6, 0 = 2*z + 6. Let n(q) be the third derivative of -1/20*q**5 - 2*q**2 - 1/2*q**4 + 0*q - i*q**3 + 0. Find p such that n(p) = 0.
-2
Let x(f) = -f + 1. Let s(d) = -4*d**2 + 105*d - 285. Let j(b) = -s(b) + 3*x(b). Let j(i) = 0. Calculate i.
3, 24
Let z(s) = 4 + 5*s + s**3 - 6 - 5*s**2 - 4*s. Let t be z(5). Find m, given that -m**t - 6*m**2 + 3 + 5*m**3 + 3 - 3*m - m**3 = 0.
-1, 1, 2
Factor -9/4*g**3 - 9/2 - 29/4*g**2 - 39/4*g - 1/4*g**4.
-(g + 1)*(g + 2)*(g + 3)**2/4
Let l(o) = -2*o - 5*o + 19*o**3 - 7*o - 12*o**2 - 7 + 19*o**4 - 5*o. Let q(v) = 6*v**4 + 6*v**3 - 4*v**2 - 6*v - 2. Let f(c) = -2*l(c) + 7*q(c). Factor f(t).
4*t*(t - 1)*(t + 1)**2
Let c(r) be the second derivative of -r**6/195 - 171*r**5/130 - 3249*r**4/26 - 61731*r**3/13 + 98*r. Factor c(g).
-2*g*(g + 57)**3/13
Factor 74/3 - 68/9*z - 2/9*z**2.
-2*(z - 3)*(z + 37)/9
Let 4 - 6*k - 4*k**3 + 2*k**5 + 37*k**4 - 3*k - 8*k**2 - 33*k**4 + 11*k = 0. Calculate k.
-2, -1, 1
Let b(s) be the third derivative of s**6/10 + 26*s**5/15 + 61*s**4/6 + 20*s**3 + 28*s**2. Solve b(a) = 0 for a.
-5, -3, -2/3
Suppose 2*h - 14 + 18 = 0, -4*m - 3*h = -14. Let s(v) be the first derivative of -6 - 4/5*v**m - v**4 + 0*v**2 + 0*v**3 + 0*v. Factor s(n).
-4*n**3*(n + 1)
Let a(j) be the second derivative of -1/90*j**6 + 0 + 1/30*j**5 - 4*j - 1/6*j**3 + 0*j**4 + 0*j**2. Let g(r) be the second derivative of a(r). Factor g(v).
-4*v*(v - 1)
Let j be (-28)/(-7) - 95/150*6. Let 0 + j*t**4 - 1/5*t**2 + 4/5*t**3 - 4/5*t = 0. Calculate t.
-4, -1, 0, 1
Let y(z) be the second derivative of -z**5/20 + z**4/4 + 2*z**3/3 - 6*z**2 + 547*z. Factor y(r).
-(r - 3)*(r - 2)*(r + 2)
Let r(j) = 5*j**4 - 41*j**3 + 94*j**2 - 68*j + 4. Let u(p) = 6*p**4 - 42*p**3 + 93*p**2 - 72*p + 6. Let x(g) = -3*r(g) + 2*u(g). Factor x(b).
-3*b*(b - 10)*(b - 2)*(b - 1)
Let i(g) = g**2 - 3*g - 6. Let t be i(5). Suppose 240*v - 240*