85/2*h**2 + 25/2*h**3 + k*h = 0.
-2, 3/5
Factor 75 - 77/2*s + 1/2*s**2.
(s - 75)*(s - 2)/2
Let 63*d + 199*d - 381*d - 4458*d**5 - 481*d + 1330*d**2 + 120*d**4 - 855*d**3 + 4463*d**5 = 0. Calculate d.
-30, 0, 1, 4
Let -27/8*i + 3/8*i**2 + 0 = 0. What is i?
0, 9
Let c be (-5 - ((-2)/4)/(22/220))/(-2). Let z(q) be the third derivative of 0 + 49/60*q**4 - 31*q**2 + c*q + 1/900*q**6 + 7/150*q**5 + 343/45*q**3. Factor z(d).
2*(d + 7)**3/15
Let n = -78164 + 78167. Factor -8/7 + 8/7*d**n + 6/7*d**2 - 8/7*d + 2/7*d**4.
2*(d - 1)*(d + 1)*(d + 2)**2/7
Let r = 782 + -764. Suppose -2*d = -3*y - r, -7*d = -6*d + 5*y + 17. Find w such that -15/2*w - 1/2*w**d - 25/2 + 9/2*w**2 = 0.
-1, 5
Let w(p) be the first derivative of -p**7/315 - p**6/45 - p**5/45 + p**4/9 + p**3/3 - 74*p**2 - 23. Let t(j) be the second derivative of w(j). Solve t(a) = 0.
-3, -1, 1
Let a(r) = 5*r**4 + 59*r**3 - 245*r**2 + 277*r. Let n(b) = 14*b**4 + 176*b**3 - 736*b**2 + 824*b. Let y(x) = 8*a(x) - 3*n(x). Factor y(i).
-2*i*(i - 2)**2*(i + 32)
Let s(p) be the first derivative of p**3 - 1350*p**2 + 2697*p - 11625. Determine v, given that s(v) = 0.
1, 899
Let v(w) be the second derivative of -w**5/20 + w**4/4 + 15*w**3 + 108*w**2 - 253*w. Let v(n) = 0. What is n?
-6, -3, 12
Factor -4/5*l**3 + 0 + 3584/5*l + 716*l**2.
-4*l*(l - 896)*(l + 1)/5
Let l = 56 - 42. Let o = l - -4. Factor -23*x**2 + o*x**2 - 22 - 8 - 35*x.
-5*(x + 1)*(x + 6)
Let n(d) be the second derivative of -d**10/15120 - d**9/3780 + d**7/630 + d**6/360 + 17*d**4/2 + 24*d. Let b(h) be the third derivative of n(h). Factor b(c).
-2*c*(c - 1)*(c + 1)**3
Find z such that 214/19*z - 2/19*z**5 - 212/19*z**3 + 106/19 + 4/19*z**2 - 110/19*z**4 = 0.
-53, -1, 1
Let k(y) be the second derivative of 3*y**7/35 + 23*y**6/25 - 42*y**5/5 - 338*y**4/5 + 48*y**3 + 54*y. Let k(u) = 0. Calculate u.
-10, -4, 0, 1/3, 6
Let q(j) = -3*j**4 + j**3 + j**2. Let c(x) = 10*x**4 - 5*x**3 + 35*x**2 - 80. Let h(k) = c(k) + 5*q(k). Find u such that h(u) = 0.
-2, 2
Let h(t) = 2*t**3 + 2*t - 1. Let z(w) = 2*w**4 - 20*w**3 + 24*w**2 + 36*w - 30. Let n(f) = 4*h(f) - z(f). Factor n(s).
-2*(s - 13)*(s - 1)**2*(s + 1)
Let w(c) be the first derivative of -c**6/18 + 13*c**5/15 + 2*c**4 - 392*c**3/9 - 680*c**2/3 - 400*c + 1293. Find t, given that w(t) = 0.
-3, -2, 10
Let h = 8155/2 + -4070. Let b(z) be the first derivative of -h*z**2 - 4 + 10*z + 5/3*z**3. Solve b(y) = 0.
1, 2
Let c be (-3 - (7 + 5))*(-2)/6. Let -2*l**3 - 8*l + 3*l + c*l**2 - 5*l**4 + 2*l**3 - 2*l**3 + 7*l**3 = 0. What is l?
-1, 0, 1
Let i(d) be the third derivative of 0*d**4 + d**2 - 1/42*d**7 + 0 + 0*d**3 + 0*d**5 - 1/336*d**8 + 0*d**6 - 3*d. Factor i(w).
-w**4*(w + 5)
What is m in 42/5*m**3 - 2/5*m**5 - 38/5*m**2 - 8*m + 0 + 38/5*m**4 = 0?
-1, 0, 1, 20
Let s(l) be the third derivative of 13*l**7/21 - l**6/30 - 13*l**5/6 + l**4/6 - 3*l**2 + 172*l. Suppose s(j) = 0. What is j?
-1, 0, 2/65, 1
Let t(u) be the first derivative of u**6/2 - 21*u**5/5 - 27*u**4/4 + 7*u**3 + 12*u**2 + 631. Factor t(h).
3*h*(h - 8)*(h - 1)*(h + 1)**2
Let f be 2/(-7) + 1/(14/32). Suppose -9*p + 0*p + 90 = 0. Factor -256*l**3 + 156*l + 29 - 16 + 33 + 64*l**f - p.
-4*(l - 1)*(8*l + 3)**2
Let p(y) = -2*y**3 - 1811*y**2 - 3634*y - 1828. Let q(j) = 6*j**3 + 5438*j**2 + 10906*j + 5482. Let d(i) = 8*p(i) + 3*q(i). Suppose d(t) = 0. What is t?
-911, -1
Suppose -372 = 4*u + 7*b - 3*b, 0 = 5*u - 4*b + 456. Let f = u + 95. Factor -7*r - f*r**2 + 3*r + 2*r.
-r*(3*r + 2)
Solve -1392/5 - 1636/5*i - 2/5*i**3 - 246/5*i**2 = 0.
-116, -6, -1
Let n(g) be the third derivative of 159*g**5/70 + 479*g**4/84 + 2*g**3/21 - 1438*g**2. Determine m, given that n(m) = 0.
-1, -2/477
Let s be ((-405)/140 - 0)/(297/(-1584)). Let 27/7*l**3 + 3/7*l**4 + s*l + 48/7 + 12*l**2 = 0. Calculate l.
-4, -2, -1
Suppose 68 = -117*w - 283. Let y be ((w/4)/(-1))/((-576)/(-1152)). Factor 2*t - y - 1/2*t**2.
-(t - 3)*(t - 1)/2
Solve -88/3*d - 1/3*d**2 - 172/3 = 0 for d.
-86, -2
Let h(r) = -9*r - 13. Let s be h(-2). Suppose 0 = -s*g - d + 9, 4*g + d - 12 = 5*d. Let 29*n**2 + 6 - 9*n - 26*n**g + 0 = 0. What is n?
1, 2
Let h(o) be the first derivative of 5*o**6/12 - 161*o**5/2 + 795*o**4/4 + 5*o**3/3 - 1595*o**2/4 + 795*o/2 + 1242. Solve h(i) = 0 for i.
-1, 1, 159
Factor -1/5*v**2 + 0 - 66/5*v**3 + 1/5*v**4 + 66/5*v.
v*(v - 66)*(v - 1)*(v + 1)/5
Let 632/3*g**3 - 28/3*g**4 - 6560/3*g + 1600/3 - 16/3*g**5 + 484/3*g**2 = 0. What is g?
-5, 1/4, 4
Let a(m) = -m**3 + 8*m**2 - 15*m + 24. Let y be a(6). Let p be ((-28)/(-7) + y)*4/15. Determine i, given that 2/3 - 5/3*i**3 - p*i**2 - 1/3*i = 0.
-1, 2/5
Let s = -523189/1372 - 1/4116. Let x = -381 - s. Let -16/3 + 0*v**2 + x*v**3 - 4*v = 0. What is v?
-2, 4
Let b(g) = -845*g - 21967. Let a be b(-26). Solve -6/7*v**4 - 6/7*v + 0 - 10/7*v**a + 22/7*v**2 = 0 for v.
-3, 0, 1/3, 1
Let a = -29 - -26. Let y(c) = 2*c**4 + 16*c**3 + 2*c**2 + 3*c. Let d(q) = -15*q**4 - 110*q**3 - 15*q**2 - 20*q. Let k(l) = a*d(l) - 20*y(l). Factor k(j).
5*j**2*(j + 1)**2
Let x(i) = 2*i**2 + i - 1. Let o(s) be the third derivative of 2/3*s**3 - 9*s**2 - 1/4*s**4 + 0*s + 0 - 1/6*s**5. Let a(w) = 3*o(w) + 14*x(w). Factor a(h).
-2*(h + 1)**2
Let b = 217752 - 217749. Determine w so that 3/4*w**2 - 1/2*w**b + 0*w - 1/4*w**4 + 0 = 0.
-3, 0, 1
Let b(j) = -6*j**2 - 156*j - 2904. Let w(p) = -p**2 - p - 4. Suppose -121 = -32*r + 7. Let o(d) = r*w(d) - b(d). Factor o(f).
2*(f + 38)**2
Let j(v) be the first derivative of 635*v**4/8 - 39*v**3 - 2*v**2 + 1028. What is i in j(i) = 0?
-4/127, 0, 2/5
Let z(c) be the first derivative of c**4/10 - 26*c**3/3 - 204*c**2/5 + 1806. Solve z(h) = 0 for h.
-3, 0, 68
Let g be ((-4)/8)/(10/(-40)). Let k(w) = -w**3 + 4*w + 2. Let s be k(g). Factor -1/4*l**s + 1/4*l + 0.
-l*(l - 1)/4
Let a(j) be the third derivative of -16 - 1/56*j**4 - 9/70*j**6 - 3*j**2 + 0*j - 13/140*j**5 + 0*j**3. Factor a(v).
-3*v*(4*v + 1)*(9*v + 1)/7
Let w be (-9 + -3)*2*1/(-8). Factor -34*z + w*z**2 + 61*z - 6*z**2 + 36 - 6.
-3*(z - 10)*(z + 1)
Factor -60*x**2 + 28*x**2 + 8839*x - 322 - 8618*x + x**3.
(x - 23)*(x - 7)*(x - 2)
Let n(z) be the third derivative of -z**8/1008 + z**7/105 + z**6/36 - 4*z**5/45 - 11*z**4/24 - 7*z**3/9 + 535*z**2. Factor n(j).
-(j - 7)*(j - 2)*(j + 1)**3/3
Factor -232/9*r**2 - 32/9*r**4 - 40/9 - 158/9*r - 148/9*r**3 + 2/9*r**5.
2*(r - 20)*(r + 1)**4/9
Solve 26/11*y**2 - 90/11 + 62/11*y + 2/11*y**3 = 0.
-9, -5, 1
Factor 24798*h**3 - 73210*h**2 + 72816*h + 2/5*h**5 - 121032/5 - 198*h**4.
2*(h - 246)**2*(h - 1)**3/5
Let l(x) be the first derivative of -14*x**3/3 - 34*x**2 + 210*x - 688. Find t such that l(t) = 0.
-7, 15/7
Let u(r) = 2*r**2 + 34*r + 62. Let p be u(-15). Factor 14*f + 42 + f**3 + 4*f**3 - 122 + 26*f + 35*f**p.
5*(f - 1)*(f + 4)**2
Factor -15/4 + 27/8*x + 3/8*x**2.
3*(x - 1)*(x + 10)/8
Let p(m) be the second derivative of -25*m**7/126 + 23*m**6/90 + 77*m**5/60 - 119*m**4/36 + 20*m**3/9 + 2*m**2/3 + m - 2888. Find d, given that p(d) = 0.
-2, -2/25, 1
Let l(c) = 19*c**2 + 342*c + 347. Let p(t) = -50*t**2 - 1028*t - 1042. Let r(i) = 8*l(i) + 3*p(i). Factor r(a).
2*(a - 175)*(a + 1)
Let r be 148/10*(-15)/(-6). Suppose r*z - 39*z + 34 = 0. Find p, given that 10*p**5 + 21*p - 54*p**3 - 5*p**4 - z*p - 16*p - p**4 - 50*p**2 = 0.
-1, -2/5, 0, 3
Let l(b) = -b**2 - 1. Let h = -40 - -44. Suppose -5*c + h*c = -1. Let q(y) = -18*y**2 + 6*y - 4. Let n(u) = c*q(u) - 8*l(u). Determine p, given that n(p) = 0.
-2/5, 1
Let v(g) be the first derivative of 0*g**2 + 0*g**5 - 6*g**3 + 1/2*g**6 + 0*g - 72 - 21/4*g**4. Factor v(q).
3*q**2*(q - 3)*(q + 1)*(q + 2)
Let q(v) be the first derivative of 5*v**4 - 445*v**3/3 - 425*v**2 + 240*v + 148. Solve q(b) = 0.
-2, 1/4, 24
Let v(p) be the second derivative of -5*p**7/231 - 19*p**6/55 - 76*p**5/55 - 2*p**4 - 32*p**3/33 + 9*p - 31. Suppose v(d) = 0. What is d?
-8, -2, -1, -2/5, 0
Let x(l) = -l**3 + 62*l**2 + 307*l + 106. Let f be x(67). Let z = f - -7083/4. Factor -3/8*o**2 - z*o + 3/4*o**3 + 3/8*o**4 + 0.
3*o*(o - 1)*(o + 1)*(o + 2)/8
Suppose 41*x + 4988 = 21224. Let i = x + -393. Solve 1/4*n**i + 1/4 - 1/4*n**2 - 1/4*n = 0.
-1, 1
Let y(p) be the third derivative of p**7/210 + 2063*p**6/600 + 821*p**5/75 - 137*p**4/10 - 222*p**2 + 2*p - 3. Determine z so that y(z) = 0.
-411, -2, 0, 2/5
Let k(c) be the second