culate h.
0, 1
Let f = 717/1105 + -29/85. Let q = 1432/13 - 110. Factor -2/13*r - q*r**2 + f.
-2*(r - 1)*(r + 2)/13
Let h be (-8)/2 - (-82 + 76). Let k(p) be the third derivative of 0*p + 0 - 8/3*p**3 + 1/5*p**5 + 4*p**h + 0*p**4 - 1/30*p**6. Suppose k(f) = 0. What is f?
-1, 2
Let r be (5 - (-252)/(-45)) + (-29)/(-15). Suppose 2*s - 6*s = 0. Factor 2/3*i**2 + r*i + s.
2*i*(i + 2)/3
Let c = -700 + 703. Factor -15*g**c + 60*g + 40 + 5/2*g**2 + 5/2*g**4.
5*(g - 4)**2*(g + 1)**2/2
Suppose -13*q + 6974 - 760 = 0. Factor -478 - 40*n**2 + 94*n + q + 4*n**3 + 6*n.
4*n*(n - 5)**2
Let g = -17022 - -50360/3. Let d = g - -238. Factor 8/3*m + d - 2*m**2.
-2*(m - 2)*(3*m + 2)/3
Let -1/3*x**5 + 3*x**3 + 0 + 1/3*x**4 + 4/3*x + 11/3*x**2 = 0. What is x?
-1, 0, 4
Let n(z) = -6*z**2 - 64*z + 185. Let w be n(-13). Let -5/7*x - 2/7 + 4/7*x**4 + 4/7*x**w - 2/7*x**2 + 1/7*x**5 = 0. What is x?
-2, -1, 1
Let s = 1887 + -1882. Solve -4/9 - 4/9*q**4 + 8/9*q**2 + 4/9*q**s + 4/9*q - 8/9*q**3 = 0 for q.
-1, 1
Suppose -357/10*b**2 + 122/5*b - 147/5*b**3 + 343/10*b**4 - 18/5 = 0. What is b?
-1, 2/7, 9/7
Suppose 119*p - 115*p = -5*i + 7, -i + p + 5 = 0. Factor 5/4*f**2 + 0 + 1/2*f - 1/2*f**i - 5/4*f**4.
-f*(f - 1)*(f + 1)*(5*f + 2)/4
Let n(h) be the third derivative of 0 - 2/15*h**5 + 0*h**3 - 2/105*h**7 + 0*h**4 - 1/10*h**6 + 12*h**2 + 0*h. Factor n(g).
-4*g**2*(g + 1)*(g + 2)
Factor 0 - 3/4*p**3 + 1/4*p**5 - 5/4*p**2 - 1/2*p + 1/4*p**4.
p*(p - 2)*(p + 1)**3/4
Let u(a) be the third derivative of a**5/180 + 7*a**4/72 + a**3/3 + 10*a**2 + 2*a. Factor u(q).
(q + 1)*(q + 6)/3
Let h(f) be the first derivative of 0*f + 2/13*f**2 - 20 - 1/13*f**4 - 2/39*f**3 + 2/65*f**5. Solve h(t) = 0.
-1, 0, 1, 2
Let x = 19 - 15. Factor 8*r + 9*r**2 - x*r**2 - r**4 + 58*r**3 - 60*r**3 - r**2.
-r*(r - 2)*(r + 2)**2
Determine b so that 3/4*b**2 + 15*b - 63/4 = 0.
-21, 1
Let q(x) be the third derivative of x**9/5040 + x**8/1120 + x**7/840 - 5*x**4/24 + 6*x**2. Let j(d) be the second derivative of q(d). Factor j(t).
3*t**2*(t + 1)**2
Let s(p) be the third derivative of 19*p**2 + 1/1365*p**7 + 0*p**6 - 1/195*p**5 + 0*p**4 + 0*p + 1/39*p**3 + 0. Determine w, given that s(w) = 0.
-1, 1
Let p(g) be the third derivative of g**6/30 + 2*g**5/5 + 73*g**2. Solve p(l) = 0 for l.
-6, 0
Let w be (3 - 5)/(12/(-6))*55. Let t be ((-630)/w)/3 - -4. What is s in 2/11*s + 2/11*s**4 - t*s**3 - 6/11*s**2 + 4/11 = 0?
-1, 1, 2
Let d be ((-242)/(-8)*-3)/((-69)/184). Suppose d + 0*w**3 - 243 + w**2 + w - w**3 = 0. What is w?
-1, 1
Let k be (((-15)/2)/(-5))/(6/20). Factor -6*h**5 + 1 + k*h**4 + 10*h**5 + h - 2*h**2 - 3*h**5 - 4*h**4 - 2*h**3.
(h - 1)**2*(h + 1)**3
Factor 1/5*n**2 - 17/5*n - 38/5.
(n - 19)*(n + 2)/5
Let m(b) be the third derivative of -b**5/45 - 11*b**4/18 + 8*b**3/3 + 87*b**2. Suppose m(p) = 0. Calculate p.
-12, 1
Let p be (1 - -2) + ((-15)/25)/(138/575). Factor 1/4*c - p + 1/4*c**2.
(c - 1)*(c + 2)/4
Let p(t) be the second derivative of t**4/66 + 17*t**3/11 + 50*t**2/11 + 7*t + 1. Factor p(w).
2*(w + 1)*(w + 50)/11
Let y(u) = -u**3 + 5*u**2 + u + 3. Let k be y(5). Factor -s**4 + k*s**5 - 4*s**5 + 6*s**4 + s**3.
s**3*(s + 1)*(4*s + 1)
Let w(t) be the third derivative of t**7/630 - t**6/120 - t**5/30 + t**4/9 - 112*t**2. Find o such that w(o) = 0.
-2, 0, 1, 4
Factor 30/19 - 58/19*q + 2/19*q**3 + 26/19*q**2.
2*(q - 1)**2*(q + 15)/19
Let g(w) be the third derivative of 0*w + 0 + 1/33*w**3 + 7/330*w**5 + 1/220*w**6 - 2*w**2 + 5/132*w**4. Factor g(m).
2*(m + 1)**2*(3*m + 1)/11
Suppose 12 = g + 2*o, -5*g + 36 = -10*o + 14*o. Suppose -g*j - 108 = -120. Let 0 - 4/5*p + 2*p**j + 18/5*p**2 = 0. Calculate p.
-2, 0, 1/5
Let -164*d**2 + 2436*d**3 - 115*d**2 - 176*d**2 - 339*d**4 + 12*d**5 - 133*d**2 = 0. Calculate d.
0, 1/4, 14
Let w(t) be the third derivative of t**5/60 + 67*t**4/24 + 11*t**3 + 60*t**2. Factor w(v).
(v + 1)*(v + 66)
Let p(j) be the first derivative of 3*j**5/25 + 17*j**4/40 + 3*j**3/5 + 11*j**2 + 12. Let u(w) be the second derivative of p(w). Let u(m) = 0. Calculate m.
-3/4, -2/3
Let l = 1339/940 + -276/235. Factor 1/2*z**3 + 0*z**4 + 0 + 0*z**2 - l*z**5 - 1/4*z.
-z*(z - 1)**2*(z + 1)**2/4
Let d(k) = -k**3 + 17*k**2 - 17*k + 19. Let l be (2/4)/((-3)/(-96)). Let q be d(l). Factor q*c**2 + 6*c**2 - 5*c**2 - 4*c.
4*c*(c - 1)
Let x = -23061 - -23064. Factor 2/13*v**2 + 0 - 2/13*v**5 + 2/13*v**x - 2/13*v**4 + 0*v.
-2*v**2*(v - 1)*(v + 1)**2/13
Let z(d) be the third derivative of d**6/24 + d**5/12 - 29*d**2 + 1. Factor z(y).
5*y**2*(y + 1)
Let t be (-70)/630*(-301 - -1)*1/5. Factor -t*n**3 - 20/3*n + 5/3 + 5/3*n**4 + 10*n**2.
5*(n - 1)**4/3
Let j = 193/402 + 4/201. Let q be (-10)/(-8) - 2 - -3. Find r, given that r**2 + j + q*r = 0.
-2, -1/4
Let j = -11 + 13. Suppose -5*g = 4*l - 6, 5*l = j*g - 2 - 7. Factor 2*k**2 + 3*k**3 - 5*k**g + 6*k**2 - 3*k - 3*k**4.
-3*k*(k - 1)**2*(k + 1)
Let g(x) be the third derivative of 1/315*x**7 - 1/504*x**8 + 0 + 0*x**3 + 0*x - 1/18*x**5 + 1/18*x**4 + x**2 + 1/60*x**6. Find c such that g(c) = 0.
-2, 0, 1
Let t(g) be the third derivative of -1/780*g**6 - 1/52*g**4 + 0 - 10*g**2 + 1/130*g**5 + 1/39*g**3 + 0*g. Factor t(l).
-2*(l - 1)**3/13
Let s(z) = z**2 - 2*z - 4. Let k be s(4). Let t be (-16)/(-2)*(k - 0). Factor t*g**2 - g - 14*g**2 - 16*g**2 - 2 + 1.
(g - 1)*(2*g + 1)
Let t be 7*((3/(-6))/(-1) - (-1547)/(-3822)). Solve t*f**2 - 2/3*f + 0 = 0.
0, 1
Factor 70*o**2 + 45*o + 11*o**2 + 35*o**3 - 5*o**4 - 156*o**2.
-5*o*(o - 3)**2*(o - 1)
Let q be -6 - (-42)/9 - ((-240)/9)/8. Factor 4/3*b + 2*b**q + 0*b**3 + 0 - 2/3*b**4.
-2*b*(b - 2)*(b + 1)**2/3
Let k be (-2)/(-12) + (-16166)/84. Let w = -192 - k. Factor 0 + 4/7*s - w*s**2.
-2*s*(s - 2)/7
Solve -1/4*w - 7/4 + 7/4*w**2 + 1/4*w**3 = 0.
-7, -1, 1
Let h(g) be the third derivative of g**5/60 - 35*g**4/8 + 52*g**3/3 - 109*g**2 - 2*g. Let h(d) = 0. What is d?
1, 104
Let y = -36 - -56. Let i be 2/20*y/8. Let 1/4*v**5 + 0*v**3 + 0*v**2 + 0*v + 0 - i*v**4 = 0. What is v?
0, 1
Solve 1/6*r**5 + r - 1/2*r**3 - 1/2*r**4 + 0 + 7/6*r**2 = 0.
-1, 0, 2, 3
Let z(j) = j**3 - 15*j**2 - 16*j - 2. Let n(x) = 6*x**3 - 91*x**2 - 97*x - 13. Let a(g) = 6*n(g) - 39*z(g). Factor a(s).
-3*s*(s - 14)*(s + 1)
Let c(i) = i - 13. Let k be c(16). Let u(q) be the second derivative of -1/54*q**4 + 0 + 0*q**2 - 2*q + 0*q**k. Factor u(o).
-2*o**2/9
Suppose 4*r - 9 = 79. Let q(f) = -f**4 + 20*f**3 - 20*f - 10. Let s(d) = -4*d**3 + 4*d + 2. Let y(a) = r*s(a) + 4*q(a). Factor y(c).
-4*(c - 1)*(c + 1)**3
Let k be (0 + 14/4)*(-512)/(-448). Let p(z) be the first derivative of -2*z - 2/3*z**3 - 1/6*z**6 + 4/5*z**5 + 6 - z**k + 5/2*z**2. Factor p(o).
-(o - 2)*(o - 1)**3*(o + 1)
Let n be 510/(-6) + (-9 - -6). Let r be 1 + -6 + (-456)/n. Let 32/11 - 16/11*o + r*o**2 = 0. Calculate o.
4
Let g(u) = -u**3 - 16*u**2 - u - 12. Let w be g(-16). Suppose 0 = 3*i + o - w, 4*o - 16 = -4*i. Suppose i - 1/4*f - 1/4*f**2 = 0. Calculate f.
-1, 0
Let c(y) be the first derivative of -y**6/40 - y**5/4 - 3*y**4/4 + 37*y**2/2 + 22. Let t(v) be the second derivative of c(v). Let t(k) = 0. Calculate k.
-3, -2, 0
Let g(w) be the third derivative of -w**8/20160 + w**7/630 - w**5/20 - w**3/3 - 5*w**2 - w. Let u(f) be the third derivative of g(f). Solve u(n) = 0 for n.
0, 8
Suppose -p - 3 = -5*k - 5*p, -12 = -3*k + p. Factor -9*b**2 + 0*b**2 - 16*b - 7*b**2 - 4*b**k.
-4*b*(b + 2)**2
Suppose -3*k - 3 + 3 = 0. Let z be (k + 6)/((-18)/(-4)*1). Factor z*p**4 + 0*p**2 + 4*p**3 + 0*p + 0.
4*p**3*(p + 3)/3
Factor -18492*d**2 + 109 + 19*d + 18493*d**2 + 21*d + 291.
(d + 20)**2
Factor -18*q**3 - 630*q + 2/3*q**4 - 198*q**2 - 648.
2*(q - 36)*(q + 3)**3/3
Let w(v) be the second derivative of 1/24*v**4 - 16*v + 0 + 1/4*v**3 + 1/2*v**2. Factor w(o).
(o + 1)*(o + 2)/2
Let x(q) = -2*q**2 + 11*q. Let t be x(5). Suppose 3*s = t*f + 4, 8 = 5*f - 0*s + s. Factor -3*g**2 + 38*g**3 - 37*g**3 + 3*g - 2 + f.
(g - 1)**3
Let j(a) be the third derivative of -a**6/80 - 66*a**5/5 - 5808*a**4 - 1362944*a**3 - 16*a**2 + 17*a. Let j(z) = 0. What is z?
-176
Let b(f) = 2*f**2 - 296*f - 4. Let i(r) = -3*r**2 + 294*r + 5. Let a(w) = -5*b(w) - 4*i(w). Solve a(t) = 0.
-152, 0
Let o(k) be the third derivative of 7*k**8/3840 + k**7/480 + k**6/960 - k**5/6 + k**2. Let d(f) be the third derivative of o(f). Factor d(u).
3*(7*u + 1)**2/4