What is z?
0, 1/3, 6
Let a(w) be the second derivative of -w**6/900 + w**5/600 + 7*w**3/6 + 14*w. Let r(q) be the second derivative of a(q). Factor r(s).
-s*(2*s - 1)/5
Suppose 0 = 2*i + 4*a, -3 - 5 = 4*i + 4*a. Let d be ((-528)/130)/i - 14/35. Let 0 - 2/13*h**3 + 8/13*h**2 - d*h = 0. What is h?
0, 2
Let u be (-252)/20*(-8 + 3). Let p be 10/30 - (-6)/u. Factor -p*a**3 + 3/7*a + 0 + 0*a**2.
-3*a*(a - 1)*(a + 1)/7
Let m = 21 + -15. Suppose 5*f + 4*r = m*r + 9, 4*f + 3*r - 21 = 0. Factor 0*b**5 - 4*b**4 + 4*b**2 + 2*b**5 + 3*b**f - 5*b**3.
2*b**2*(b - 2)*(b - 1)*(b + 1)
Suppose -2*r + 3*r**3 - 15 - 2723*r**2 + 65 + 2673*r**2 - r**3 = 0. Calculate r.
-1, 1, 25
Let l be (-5 - -4)/(((-6)/(-3))/8). Let o(m) = -3*m**3 + 2*m**2 + 4*m. Let c(d) = 4*d**3 - 3*d**2 - 4*d. Let y(j) = l*c(j) - 6*o(j). Factor y(s).
2*s*(s - 2)*(s + 2)
Let p be (-28)/35*30/(-12). Let u(c) be the first derivative of -13/10*c**4 + 3 + 8/25*c**5 + 0*c + 22/15*c**3 - 2/5*c**p. Solve u(l) = 0.
0, 1/4, 1, 2
Let i = -22/57 + 85/171. Let k(o) be the second derivative of -3*o - i*o**3 + 0 + 1/36*o**4 + 1/6*o**2. Factor k(l).
(l - 1)**2/3
Let 2/13*p**5 + 18/13*p**3 + 0 - 14/13*p**2 - 10/13*p**4 + 4/13*p = 0. Calculate p.
0, 1, 2
Suppose -c = 3*c - 24. Let z(y) = 3*y - 16. Let j be z(c). Determine b so that -4/15 + 6/5*b - 14/15*b**j = 0.
2/7, 1
Let z(r) be the second derivative of 19*r + 2/7*r**2 + 5/7*r**4 + 0 + 19/21*r**3. Determine h so that z(h) = 0.
-1/2, -2/15
Let x(m) be the third derivative of m**7/420 + 11*m**6/720 + m**5/60 + 44*m**2. Factor x(g).
g**2*(g + 3)*(3*g + 2)/6
Let b(c) = 2*c**5 - c**3 - c - 1. Let x(d) = 7*d**5 - 7*d**4 - 12*d**3 + 16*d**2 - 4*d - 4. Let r(z) = -4*b(z) + x(z). Find m, given that r(m) = 0.
-4, 0, 1
Let t(k) be the first derivative of 0*k - 3/4*k**2 - 12 + 1/4*k**3. What is g in t(g) = 0?
0, 2
Solve -32/9 + 2/9*n**3 - 32/9*n + 2/9*n**2 = 0 for n.
-4, -1, 4
Let c(o) = -4*o**3 + 68*o**2 - 3*o + 53. Let j be c(17). Factor -4/3*v**4 + 0 + 8/3*v**3 + 0*v + 0*v**j.
-4*v**3*(v - 2)/3
Suppose 4*z - 6 = i - 22, -4*z = -3*i + 24. Suppose -4*v + 4*a - i = 0, v = -3*a + 12 + 3. Factor t**4 - 101*t**3 + 89*t**v - 2*t**4 + 12*t**2 + 4*t**4.
3*t**2*(t - 2)**2
Let j = -2 + 4. Suppose 5*m + 4*b - 2*b - 15 = 0, -2*m = -j*b - 6. Determine k, given that 2*k**2 - 2/5*k**m - 16/5*k + 8/5 = 0.
1, 2
Let d(j) be the third derivative of 0*j + 5/72*j**5 + 0 - 1/9*j**4 - 19/720*j**6 - 3*j**2 - 1/2016*j**8 + 1/9*j**3 + 1/180*j**7. Factor d(u).
-(u - 2)**2*(u - 1)**3/6
Factor 40*h**2 - 47*h**4 - 9*h**5 - 43*h**4 - 20*h**5 - 60*h**3 + 4*h**5.
-5*h**2*(h + 2)**2*(5*h - 2)
Factor 3*s**4 - 7*s**4 - 12*s + 4*s**5 + 12*s.
4*s**4*(s - 1)
Let a(i) = 5*i**2 + 125*i - 130. Let f(g) = 10*g**2 + 250*g - 260. Let w(n) = -5*a(n) + 3*f(n). Solve w(u) = 0.
-26, 1
Let n(l) be the second derivative of -l**6/50 - 7*l**5/50 - 17*l**4/60 - l**3/5 + 871*l. Determine h, given that n(h) = 0.
-3, -1, -2/3, 0
Suppose 0*y + 56 = 2*y. Suppose -4*g**2 - 3*g - 3*g + 10 - g**3 + y*g - 15*g = 0. What is g?
-5, -1, 2
Determine f so that 0 + 2/11*f**4 - 54/11*f**3 - 50/11*f + 102/11*f**2 = 0.
0, 1, 25
Let a(w) = w**3 + w**2 - 1. Let y(m) = -25*m**2 + 25*m - 5. Suppose -4*p - 4 = -0*p. Let g(j) = p*y(j) - 5*a(j). Factor g(f).
-5*(f - 2)*(f - 1)**2
Let j(z) = -312*z - 3744. Let y be j(-12). Solve 0*c + 3/2*c**4 + c**3 + y + 1/2*c**5 + 0*c**2 = 0.
-2, -1, 0
Let s(o) = -8*o + 13*o**2 - 4*o**2 + 4 + 8*o + o**3. Let a be s(-9). Determine l, given that -5 + 199*l**3 - 315*l**2 + 108*l - 135*l**a + 155*l**3 - 7 = 0.
2/9, 2/5, 1
Let a(q) = q**2 + 57*q + 432. Let r be a(-48). Factor 9/5*i**2 + r + 3/5*i**4 - 3/5*i - 9/5*i**3.
3*i*(i - 1)**3/5
Let r(p) be the first derivative of p**4/28 + 4*p**3/21 - 11*p**2/14 + 6*p/7 - 65. Factor r(j).
(j - 1)**2*(j + 6)/7
Let x be 3/((-378)/(-33)) + 1/(-4). Let s(y) be the third derivative of -y**2 + 0*y**7 + 0*y**4 + 0 + 0*y**5 + 0*y**3 + 0*y**6 + 0*y - x*y**8. Factor s(w).
-4*w**5
Solve 8/5 - 2/5*m + 2/5*m**3 + 1/5*m**4 - 9/5*m**2 = 0.
-4, -1, 1, 2
Let j(h) = -h + 10. Let r be j(8). Suppose -2*c + r = -c. Factor -3 - 33*g + c - 27*g**2 - 5 + 0.
-3*(g + 1)*(9*g + 2)
Let y(q) be the second derivative of -q**8/1260 + q**7/315 - q**6/270 - 2*q**3 - 10*q. Let g(b) be the second derivative of y(b). Factor g(l).
-4*l**2*(l - 1)**2/3
Let m be ((-15)/12)/(0 - (-2)/(-40)). Let y be m/68 + 18/(-153). Solve 0 + y*l**4 + 1/4*l**3 + 0*l + 0*l**2 = 0.
-1, 0
Let r be 0 - ((-23)/6 - (-1)/(-6)). Suppose -q = -2*c - 0*q + 8, -r*c + 14 = -q. Solve -2/3*v**c - 4/3*v**2 - 2/3*v + 0 = 0 for v.
-1, 0
Suppose -5*m + 72 + 145 = -3*f, 5*m - 222 = -2*f. Determine o so that m + 2*o**2 - 28*o + 23 + 31 = 0.
7
Let r = -2/15 + 11/15. Let x(q) be the first derivative of -r*q**5 + 15/4*q**4 + 12*q - 1/2*q**6 + q**3 - 12*q**2 - 5. Suppose x(i) = 0. What is i?
-2, 1
Let r(z) be the third derivative of z**5/270 + 7*z**4/108 - 8*z**2 + 12*z. Factor r(y).
2*y*(y + 7)/9
Let a(y) be the third derivative of -y**6/1320 + 23*y**5/660 - 13*y**4/24 + 11*y**3/6 + 123*y**2. Suppose a(f) = 0. Calculate f.
1, 11
Let c(h) be the third derivative of h**9/75600 + h**8/25200 - h**5/30 - 8*h**2. Let x(g) be the third derivative of c(g). Determine i, given that x(i) = 0.
-1, 0
Let k(x) be the third derivative of -x**6/120 + 2*x**5/3 - 13*x**4/8 + x**2 + 2. Factor k(z).
-z*(z - 39)*(z - 1)
Let -3/7*t**2 - 9/7 - 12/7*t = 0. Calculate t.
-3, -1
Suppose 30*h = 93*h - 252. Let u(y) be the first derivative of -6 + 0*y - 16/3*y**3 - 308/5*y**5 + 0*y**2 - 98/3*y**6 - 32*y**h. Factor u(f).
-4*f**2*(f + 1)*(7*f + 2)**2
Let l(c) be the first derivative of 2*c**5/35 - c**4/7 - 38*c**3/21 - 4*c**2 - 24*c/7 - 478. Factor l(s).
2*(s - 6)*(s + 1)**2*(s + 2)/7
Factor 1/4*o**2 - 10 + 3/2*o.
(o - 4)*(o + 10)/4
Let q(o) be the first derivative of o**6/240 - o**5/60 - o**4/48 + o**3/6 + 15*o**2/2 + 5. Let d(x) be the second derivative of q(x). Factor d(r).
(r - 2)*(r - 1)*(r + 1)/2
Let l be (0 - -3)/(6/(-16)) + 14. Factor -3*z**4 + 9/2*z**3 + 6*z**2 + 0 - 3/2*z**5 - l*z.
-3*z*(z - 1)**2*(z + 2)**2/2
Let c(b) be the second derivative of b**4/42 - 8*b**3/21 + 16*b**2/7 - 10*b - 8. Factor c(r).
2*(r - 4)**2/7
Let n(m) be the third derivative of m**7/630 - m**6/135 + m**5/90 + 7*m**3/2 + 3*m**2. Let z(i) be the first derivative of n(i). Solve z(r) = 0.
0, 1
Let w = 19 + -12. Suppose -o - 5*x + 0*x = -13, x = 3*o - w. Find y such that 0 + 5/6*y**4 + 1/3*y**2 + 0*y + 7/6*y**o = 0.
-1, -2/5, 0
Let i(j) be the first derivative of j**5/90 + j**4/9 + j**3/3 - 5*j - 7. Let l(t) be the first derivative of i(t). Factor l(g).
2*g*(g + 3)**2/9
Factor 16*g + 17*g**2 + 22 - 21*g**2 - 34 + 0.
-4*(g - 3)*(g - 1)
Let r = -1 + 4. Suppose -5*z - 9 = -x + 15, 3*x - r*z - 24 = 0. Suppose 3*d**x - 13*d**4 + 0*d**2 + 12*d**4 - 2*d**2 - 2*d**3 + 2*d = 0. Calculate d.
-1, 0, 1
Let p(g) be the first derivative of 2*g**5/65 + 2*g**4/13 - 2*g**3/13 - 18*g**2/13 - 97. Determine k, given that p(k) = 0.
-3, 0, 2
Suppose -752*i + 753*i = 5*j - 8, j = -i - 8. What is c in j + 1/10*c**2 - 1/5*c + 1/10*c**3 = 0?
-2, 0, 1
Let b(u) be the first derivative of 13*u**4/66 + 28*u**3/33 + 4*u**2/11 + 11*u + 46. Let m(l) be the first derivative of b(l). Factor m(h).
2*(h + 2)*(13*h + 2)/11
Determine u, given that 138 - 6*u**3 - 64*u**2 + 8*u**3 + 570*u - 1038 = 0.
2, 15
Let k(n) = 7*n + 41. Let a be k(-8). Let s be -1 - (a/(-9) - 4). Solve -2/3*u**5 - 32/3*u**2 - 4*u**4 - 28/3*u**3 - 6*u - s = 0.
-2, -1
Let w(p) be the first derivative of -1/6*p**6 + 0*p**3 + 1/4*p**4 - 14 + 0*p**5 + 0*p + 0*p**2. Determine a so that w(a) = 0.
-1, 0, 1
Suppose 4*d - 16 = 0, -d + 11 + 1 = 2*u. Factor 4*a**5 + 8*a**3 - 6*a**4 + 0 - 4*a**2 - 12*a + 18*a**4 - u*a**2 - 4.
4*(a - 1)*(a + 1)**4
Solve -4 + 40*g**2 + 78 + 6 - 100*g - 5*g**3 = 0 for g.
2, 4
Let j = -1555 - -1555. What is a in 8*a**2 - a**4 + j - 2*a + 5/2*a**5 - 15/2*a**3 = 0?
-2, 0, 2/5, 1
Factor 421*b**5 - 212*b**5 + 36*b**2 + 28*b**4 + 60*b**3 - 205*b**5.
4*b**2*(b + 1)*(b + 3)**2
Let q(g) be the first derivative of 35*g**3/3 + 4805*g**2/2 + 1370*g - 186. Determine j, given that q(j) = 0.
-137, -2/7
Let u = 72 - 69. Let g = -1 + u. Suppose 1 - 43/2*j**3 - j**g + 15*j**4 + 13/2*j = 0. What is j?
-2/5, -1/6, 1
Factor -43*y**2 + 222*y**3 - 194*y - 45*y**4 - 31*