4)/8
Determine x so that -32 + 32/3*x**2 - 76/3*x + 13/3*x**3 + 1/3*x**4 = 0.
-8, -6, -1, 2
Find i, given that 167*i + 85/2*i**2 + 166 + 1/4*i**3 = 0.
-166, -2
Solve -16*u - 8*u**3 + 0 + 116/5*u**2 + 4/5*u**4 = 0.
0, 1, 4, 5
Let w = 891577/3 + -297175. Find j, given that -3*j**2 - w - 1/3*j**3 + 16*j = 0.
-13, 2
Let k(h) = 10*h - 80. Let w be k(10). Factor 32*l - 48 - w*l - 96*l**2 + 144*l + 15*l**3.
3*(l - 4)*(l - 2)*(5*l - 2)
Let y(v) be the third derivative of 34*v**2 - 64/51*v**4 + 0 + 0*v**3 + 0*v - 1/1020*v**6 - 16/255*v**5. Factor y(z).
-2*z*(z + 16)**2/17
Let a be 21/9*(-21)/(-343)*21. Determine y so that 96*y**4 + 120*y**a + 69/2*y - 126*y**2 - 3 = 0.
-2, 1/4
Let i(v) be the second derivative of v**6/10 - 33*v**5/20 - 13*v**4/4 + 11*v**3/2 + 18*v**2 + 273*v. Let i(q) = 0. What is q?
-1, 1, 12
Let n(r) be the second derivative of -3/8*r**4 - 34*r - 21*r**2 + 0 + 0*r**3 + 1/20*r**5. Let g(s) be the first derivative of n(s). Factor g(u).
3*u*(u - 3)
Let l(g) be the first derivative of -4*g**3/3 + 314*g**2 + 2368. Factor l(s).
-4*s*(s - 157)
Suppose 117*y + 10 = 122*y. Factor y*o**2 - 6 - 11*o**2 - 4 - 9*o + 10*o**2.
(o - 10)*(o + 1)
Suppose 0 = 5*h + 2*p - 97, 3*h - 762*p = -761*p + 56. Let s(a) be the second derivative of 0 - 1/21*a**4 + h*a - 4/7*a**3 + 0*a**2. Factor s(d).
-4*d*(d + 6)/7
Let c(v) be the second derivative of 3*v**6/10 + 33*v**5/4 + 15*v**4/4 - 55*v**3/2 - 27*v**2 + 99*v - 2. Suppose c(h) = 0. Calculate h.
-18, -1, -1/3, 1
Let c(h) be the first derivative of h**4/4 - 220*h**3/9 - 373*h**2/6 - 50*h - 1093. Solve c(l) = 0.
-1, -2/3, 75
Let r(y) = 1659*y + 428027. Let m be r(-258). Let -8/7*u**3 + 10/7*u - 4/7*u**2 - 2/7*u**m - 4/7 + 8/7*u**4 = 0. What is u?
-1, 1, 2
Let q(h) be the third derivative of h**7/630 + 23*h**6/180 + 11*h**5/15 + h**4/3 + h**3/6 + 127*h**2. Let u(a) be the second derivative of q(a). Solve u(r) = 0.
-22, -1
Suppose 30*l**2 + 228 + 226*l + 31*l**2 + 21*l**2 - 84*l**2 = 0. What is l?
-1, 114
Let i be 66 - 15/(-20)*(-40)/6. What is b in i*b - 18*b - 38*b + 6*b**2 + b**3 = 0?
-5, -1, 0
Let w(q) = 7*q**2 - q - 1. Let v(m) = -6*m**2 + 5*m + 1. Let a = 979 - 983. Let y(u) = a*v(u) - 4*w(u). Solve y(r) = 0.
-4, 0
Let i(o) be the second derivative of -o**5/60 - 193*o**4/6 - 74498*o**3/3 - 28756228*o**2/3 - 120*o - 26. Factor i(l).
-(l + 386)**3/3
Let p(i) be the first derivative of -5*i**6/6 - 33*i**5/5 - 51*i**4/4 + 41*i**3/3 + 42*i**2 - 36*i - 1480. Let p(n) = 0. What is n?
-3, -2, 2/5, 1
Let c be 5 + (-57)/12 - (3 - (-69)/(-12)). Let p(u) be the third derivative of 1/16*u**5 + 0*u + 1/16*u**4 - 3/8*u**c + 0 - 6*u**2. Factor p(t).
3*(t + 1)*(5*t - 3)/4
Let g(z) be the first derivative of -z**5/5 - 15*z**4/4 + 16*z**3/3 - 2363. Factor g(u).
-u**2*(u - 1)*(u + 16)
Let s(j) be the second derivative of -1/10*j**5 - j - 35/27*j**3 - 1/135*j**6 + 11/18*j**4 + 13 + 4/3*j**2. Solve s(b) = 0 for b.
-12, 1
Let o(i) be the first derivative of i**4/16 + 5*i**3/8 + 9*i**2/4 - 30*i - 16. Let p(w) be the first derivative of o(w). Find s, given that p(s) = 0.
-3, -2
Let h = 3691/2305 + -3/2305. Let t(l) be the first derivative of 0*l**2 + 11 + h*l - 2/15*l**3. Determine g so that t(g) = 0.
-2, 2
Determine b so that -1737/2*b + 3/4*b**2 + 0 = 0.
0, 1158
Let k be 17/(119/14)*-1. Let b be 14/k + (-116)/(-16). Suppose 0*d - 1/8*d**5 - 1/4*d**2 + 1/8*d**3 + 0 + b*d**4 = 0. What is d?
-1, 0, 1, 2
Let y(w) be the third derivative of w**6/480 + 233*w**5/16 + 1357225*w**4/32 + 1581167125*w**3/24 + 744*w**2 + 3*w - 1. Factor y(z).
(z + 1165)**3/4
Let x = -185655/133 + 9859/7. Let w = 2008/133 - x. Factor -3/7*v**2 - w*v - 27/7.
-3*(v + 3)**2/7
Let w be (484/(-66))/(11/(-3)). Let j(a) be the second derivative of 41*a + 4/9*a**w + 1/9*a**3 + 0 - 1/54*a**4. Factor j(k).
-2*(k - 4)*(k + 1)/9
Let h(p) = p**3 + 4*p**2 - 7*p - 3. Let v be h(-5). Let b(j) = -2*j**3 + 14*j**2 + j - 4. Let g be b(v). Factor 40/9*q + 14/9*q**g - 16/9 - 4*q**2 - 2/9*q**4.
-2*(q - 2)**3*(q - 1)/9
Factor -716*t**3 - 7*t + 10*t**2 + 719*t**3 - 189 + 11*t**2 - 20*t.
3*(t - 3)*(t + 3)*(t + 7)
Suppose -3*a + 5*l = 35, -2*l + 15 = a + 3*l. Let y(d) = -16*d - 78. Let j be y(a). Let 67*n**2 - 3*n + j + 2 - 68*n**2 = 0. Calculate n.
-4, 1
Let i(b) = 20*b**3 - 5292*b**2 + 1742392*b + 1747684. Let r(f) = -44*f**3 + 10586*f**2 - 3484783*f - 3495368. Let y(x) = 9*i(x) + 4*r(x). Solve y(d) = 0.
-1, 661
Let x be 5 + -3 - -12 - 8. Let 6 + 15*o**3 - 24*o - 6*o**2 - 19*o**4 + 0 + 16*o**4 - x = 0. Calculate o.
-1, 0, 2, 4
Let i(j) = 15*j**2 + 1785*j**4 + 7*j - j**3 - 8 - 1792*j**4 - 3*j**2. Let m(s) = s**4 - s**3 - s. Let u(k) = -i(k) - 3*m(k). Factor u(l).
4*(l - 1)**2*(l + 1)*(l + 2)
Let n be ((10/(-50))/((-2)/4))/(94/705). Let z be (4/(-66))/(2/(-6)). Suppose -z*m**2 + 0 - 4/11*m + 2/11*m**n = 0. What is m?
-1, 0, 2
Let j = -738009/7 + 105430. Factor -j*z**3 + 1/7*z**2 + 5/7*z + 3/7.
-(z - 3)*(z + 1)**2/7
Let x = -14 + 21. Suppose x*g - 40 = -12. Determine d, given that d**g - 2*d**4 + 5*d**2 - 4*d**4 = 0.
-1, 0, 1
Let a be (-18)/(-10)*283/849. Factor -4/5*m + 2/5*m**4 - 4/5*m**2 - 1/5*m**5 + a*m**3 + 0.
-m*(m - 2)**2*(m + 1)**2/5
Let b(r) = 3*r**2 - 13*r + 8. Let l be b(8). Let f = -92 + l. Factor k**f + 2/3*k**3 - 4/3*k**2 - 2/3*k + 1/3.
(k - 1)*(k + 1)**2*(3*k - 1)/3
Let s(n) be the first derivative of 6*n**5/5 + 415*n**4 - 3896*n**3/3 + 1394*n**2 - 558*n - 4173. Solve s(j) = 0 for j.
-279, 1/3, 1
Let i = 763 + -761. Let x be (-5)/(1080/(-198)) + i/(-3). Determine g, given that -x*g**4 - 3/4*g**3 + 1/2*g + 0 + 1/4*g**5 + 1/4*g**2 = 0.
-1, 0, 1, 2
Let d(h) be the first derivative of 1/20*h**4 - 1/15*h**3 + 56 + 1/25*h**5 - 1/10*h**2 + 0*h. Find z such that d(z) = 0.
-1, 0, 1
Suppose 0 = 127*l + 70 - 373 - 78. Factor -25/4 + 1/4*c**l - 11/4*c**2 + 35/4*c.
(c - 5)**2*(c - 1)/4
Let c(n) = -336*n + 13106. Let y be c(39). Factor -81/2*o**3 + 0*o + 2187/4*o**y + 0 + 3/4*o**4.
3*o**2*(o - 27)**2/4
Let h = -449807 - -449810. Suppose 28/3*q**2 + 4/3*q - 32/3 + h*q**3 = 0. Calculate q.
-2, 8/9
Let z(a) be the third derivative of a**7/105 - 1499*a**6/120 + 12475*a**5/2 - 7765625*a**4/6 - 7812500*a**3/3 - a**2 + 144*a. Factor z(q).
(q - 250)**3*(2*q + 1)
Let w = 7142/1383 + 78/461. Factor -w*d + 10/3 + 2/15*d**4 + 16/15*d**3 + 4/5*d**2.
2*(d - 1)**2*(d + 5)**2/15
Solve -2*i**2 + 4/3*i + 0 + 2/3*i**4 + 0*i**3 = 0.
-2, 0, 1
Let r(v) = 1578 + 50*v**2 - 210 + 2832 - 1155*v. Suppose -11*i - 23 = -1. Let b(c) = 3*c**2 - 68*c + 247. Let q(x) = i*r(x) + 35*b(x). Factor q(d).
5*(d - 7)**2
Let l(y) be the first derivative of y**5/30 - y**3/3 + 33*y**2/2 + 3. Let z(n) be the second derivative of l(n). Find m such that z(m) = 0.
-1, 1
Let m(c) be the first derivative of 16*c**6/15 - 264*c**5/25 - 1013*c**4/5 - 2324*c**3/3 - 3504*c**2/5 - 1088*c/5 + 11098. Determine z, given that m(z) = 0.
-4, -1/2, -1/4, 17
Let l(q) be the second derivative of 8/11*q**2 + 1/66*q**4 + 199*q + 0 - 3/11*q**3. Factor l(b).
2*(b - 8)*(b - 1)/11
Let h = 22985 + -252833/11. Determine o so that 0*o + 4/11*o**5 + 0 + h*o**3 - 6/11*o**4 + 0*o**2 = 0.
0, 1/2, 1
Suppose -12 + 291/4*n + 219/4*n**3 - 3*n**4 - 225/2*n**2 = 0. What is n?
1/4, 1, 16
Let z(x) = 2*x**2 - 13. Let d be z(-3). Let k(c) be the third derivative of -2/45*c**d - 3*c**2 + 0*c**3 + 0*c + 1/180*c**6 + 0 + 1/12*c**4. Factor k(j).
2*j*(j - 3)*(j - 1)/3
Let u(m) be the first derivative of 35*m**4/2 + 25*m**3 - 135*m**2/2 - 10*m + 2084. Solve u(l) = 0.
-2, -1/14, 1
Let n(a) = -36*a**3 - 450*a**2 + 264*a + 510. Let g(p) = 7*p**3 + 88*p**2 - 53*p - 102. Let y(x) = -21*g(x) - 4*n(x). Suppose y(i) = 0. Calculate i.
-17, -1, 2
Let d = -33 - -152. Solve -47*m**4 + 20*m**3 - d*m**4 + 66*m**4 + 105*m**5 = 0 for m.
0, 2/7, 2/3
Let y(v) = -8*v**3 + 36*v**2 + 3*v - 76. Let w be y(4). Suppose -1/5*l**5 + 0*l - 6/5*l**2 + 7/5*l**3 + 0*l**4 + w = 0. Calculate l.
-3, 0, 1, 2
Factor 0 - 58/7*k**3 + 100*k**2 - 48/7*k.
-2*k*(k - 12)*(29*k - 2)/7
Let t(i) be the first derivative of -i**4/10 - 37*i**3/15 + 59*i**2/10 - 4*i - 227. Solve t(m) = 0.
-20, 1/2, 1
Let 297/4*f**2 + 153 - 228*f + 3/4*f**3 = 0. What is f?
-102, 1, 2
Let h(v) be the third derivative of -v**5/510 + 31*v**4/204 - 58*v**3/51 - 1790*v**2. Factor h(y).
-2*(y - 29)*(y - 2)/17
Let l(m) be the first derivative o