e of z(q). Suppose a(n) = 0. Calculate n.
3
Let i(o) be the second derivative of 2/3*o**4 - 4*o**2 - 3 - 2/3*o**3 + 2*o + 1/5*o**5. Factor i(t).
4*(t - 1)*(t + 1)*(t + 2)
Suppose 8584*i - 20 = 8579*i. Let l(m) be the second derivative of -3/4*m**i + 15*m + 1/2*m**2 + 0*m**3 + 0. Determine t so that l(t) = 0.
-1/3, 1/3
Suppose -380*k - 57*k = -87*k - 700. What is a in -8/11*a**5 + 10/11*a - 38/11*a**3 - 8/11*a**k - 32/11*a**4 + 4/11 = 0?
-2, -1, -1/2, 1/2
Let r(h) be the first derivative of -h**5/20 + 105*h**4/16 - 701*h**3/12 + 1479*h**2/8 - 441*h/2 + 3867. Factor r(g).
-(g - 98)*(g - 3)**2*(g - 1)/4
Suppose 15*t = 6*t + 27. Let o(g) = 15*g**2 - 841*g**3 - 40 - t*g + 840*g**3 - 25*g. Let l(a) = a**2 - a - 1. Let v(c) = 4*l(c) - o(c). Factor v(b).
(b - 6)**2*(b + 1)
Determine l, given that -167*l**2 - 77*l**2 - 15*l**4 + 206*l**3 + 252 + 47*l**2 + 516*l - 220*l**2 - 542*l**3 = 0.
-21, -2, -2/5, 1
Let t(n) be the first derivative of -2*n**3/5 - 49*n**2/5 + 68*n/5 + 1629. Factor t(w).
-2*(w + 17)*(3*w - 2)/5
Let o(t) = -17*t**4 - 54*t**3 + 278*t**2 - 179*t - 5. Let j(w) = 18*w**4 + 57*w**3 - 276*w**2 + 177*w + 6. Let y(k) = -5*j(k) - 6*o(k). Factor y(c).
3*c*(c - 3)*(c + 7)*(4*c - 3)
Let h(w) be the third derivative of 0 - 1/24*w**5 + 4*w**3 - 1/72*w**6 + 0*w + 5/4*w**4 - 8*w**2. Let q(m) be the first derivative of h(m). Factor q(l).
-5*(l - 2)*(l + 3)
Let v = 177414 - 177411. Factor 34/9*l - 20/9*l**2 + 2/9*l**v - 16/9.
2*(l - 8)*(l - 1)**2/9
Let f(q) = -2*q**3 + 1043*q**2 + 2101*q + 1083. Let s(b) = -3*b**3 + 2088*b**2 + 4200*b + 2154. Let r(n) = 5*f(n) - 3*s(n). Find u such that r(u) = 0.
-1047, -1
Let d(c) = -6*c - 22. Let n be d(-4). What is h in -23*h**n - 2*h**2 + 54*h**4 - 49*h**4 + 20 = 0?
-2, -1, 1, 2
Let c = 902399 + -902399. Factor -32/3*u + c - 20/3*u**2 - 2/3*u**3.
-2*u*(u + 2)*(u + 8)/3
Let q(r) be the first derivative of 0*r + 7*r**2 - 5/96*r**4 + 1/240*r**5 + 1/480*r**6 + 1/8*r**3 - 17. Let m(c) be the second derivative of q(c). Factor m(y).
(y - 1)**2*(y + 3)/4
Let l(s) be the second derivative of -s**4/54 + 16*s**3/27 + 161*s**2/9 - 2*s + 1263. Suppose l(k) = 0. Calculate k.
-7, 23
Let o be 13/(91/(-28)) - 211/(-1). Factor -4*v**2 + v**2 + o*v + 99 + 6*v**2 + 93 + 12.
3*(v + 1)*(v + 68)
Determine p so that -100/7*p**2 + 64/7*p + 192/7 + 26/7*p**3 - 2/7*p**4 = 0.
-1, 4, 6
Let w(y) be the first derivative of y**7/2520 + 7*y**6/1080 + y**5/24 + y**4/8 - 26*y**3/3 - y - 47. Let i(s) be the third derivative of w(s). Factor i(b).
(b + 1)*(b + 3)**2/3
Let k = 480 - 474. Let t be (5/(-25))/(k/(-50)). What is a in 1/6*a**2 + t*a + 25/6 = 0?
-5
Suppose 575/3*l**2 - 8*l + 361/3*l**5 - 47*l**3 - 48 - 209*l**4 = 0. What is l?
-12/19, 1
Let i = -7384 - -7416. Let x(v) be the second derivative of 0*v**3 + 0*v**5 + i*v + 0 + 1/120*v**6 - 1/24*v**4 + 1/8*v**2. Find s, given that x(s) = 0.
-1, 1
Let x(p) be the second derivative of -2/15*p**6 - 512*p**2 - 4/3*p**4 - 12/5*p**5 + 0 + 128*p**3 + 43*p. Find q such that x(q) = 0.
-8, 2
Let j(h) = -11*h - 16. Let k(w) = 17*w + 24. Let f(o) = 8*j(o) + 5*k(o). Let r be f(-4). Let -7*c + 3*c + r*c**3 + 508*c**4 + 2 - 510*c**4 = 0. What is c?
-1, 1
Suppose 4*t = -2*v + 16, v + 4 - 40 = 5*t. Let n be -7 + (21 - 0)*v/48. Factor -4/7*b**3 - 2/7*b**4 - 2/7*b**2 + 0*b + n.
-2*b**2*(b + 1)**2/7
Determine z, given that -6/5*z**3 - 174/5*z**2 + 1488/5 + 84*z = 0.
-31, -2, 4
Let q = -132 + 172. Suppose q + 45 = 17*s. Factor 8/3*v**2 - 50/9*v**s + 0 + 22/9*v**3 - 20/3*v**4 - 8/9*v.
-2*v*(v + 1)**2*(5*v - 2)**2/9
Let b be ((-132)/6 - 2214/(-99))/(6/11). Let -46/3*h**3 + 0 + 22*h**2 - 28/3*h + 2*h**4 + b*h**5 = 0. Calculate h.
-7, 0, 1, 2
Let j(a) be the second derivative of a**7/21 + 104*a**6/15 + 10*a**5 - 155*a**4/3 - 101*a**3/3 + 206*a**2 - 4866*a. Let j(o) = 0. What is o?
-103, -2, -1, 1
Let -13*q**2 + 24*q**2 - 4*q**2 + 726*q - 4*q**2 - 6*q**2 - 43923 = 0. Calculate q.
121
Suppose -12 = 3*k - i, k = 3*i - 557 + 521. Suppose 117/7*c**2 - 6/7*c + k = 0. What is c?
0, 2/39
Let f be ((-50)/(-825))/(280/77). Let w(g) be the third derivative of 0 - f*g**5 + 0*g - 1/8*g**4 + 7*g**2 + 5/3*g**3. Let w(h) = 0. Calculate h.
-5, 2
Let j(g) be the third derivative of g**7/105 + 7*g**6/20 + 19*g**5/10 + 55*g**4/12 + 6*g**3 - 353*g**2. Find i, given that j(i) = 0.
-18, -1
Let j(d) be the first derivative of 3*d**4/4 + 60*d**3 - 1893*d**2/2 - 2070*d - 6152. Determine s so that j(s) = 0.
-69, -1, 10
What is x in 125*x**5 + 192*x + 84*x**3 + 133*x**5 + 26*x**4 - 259*x**5 + 97*x**3 + 346*x**2 = 0?
-3, -2, -1, 0, 32
Suppose -z + 13 = -3*c, 4*z = 3*c + c + 28. Factor 0*l + 1/2*l**5 + l**2 + 0 + 2*l**z + 5/2*l**3.
l**2*(l + 1)**2*(l + 2)/2
Factor -4*l - 47*l + 4*l**2 + 207*l + 12*l + 0*l**2.
4*l*(l + 42)
Let k be (-6 + 3)/((-200)/(-32) + -7). Suppose 4*w = 80 + 468. Factor 127 + 2*c**4 - w - 13*c - 24*c**2 - k*c**3 - 15*c.
2*(c - 5)*(c + 1)**3
Let l(i) be the second derivative of -3*i**5/20 - 3*i**4/2 - 5*i**3/2 + 8*i - 1. Let w(p) = -2*p**3 - 17*p**2 - 15*p. Let x(j) = -3*l(j) + 2*w(j). Factor x(n).
5*n*(n + 1)*(n + 3)
Let b(n) be the third derivative of -n**6/240 + n**5/24 + 25*n**4/48 - 125*n**3/12 + 109*n**2 + 2. Determine s, given that b(s) = 0.
-5, 5
Suppose 1574*n = 1577*n - 15. Let s(z) be the first derivative of -8/21*z**3 + 0*z**2 - 7/3*z**6 + 14/5*z**n - 1 + 0*z + 2/7*z**4. Find b, given that s(b) = 0.
-2/7, 0, 2/7, 1
Let t = 93 - 91. Suppose t*h - 20*c + 12 = -16*c, 0 = 3*c - 9. What is v in -v + h + 1/2*v**2 = 0?
0, 2
Let h(v) be the second derivative of v**6/21 - 16*v**5/35 + 67*v**4/42 - 52*v**3/21 + 12*v**2/7 + v - 480. Suppose h(s) = 0. Calculate s.
2/5, 1, 2, 3
Let d be 14/((-3192)/(-1406)) - 6. Let -1/2*y**4 + 1/6*y**5 + 0 + 0*y - d*y**2 + 1/2*y**3 = 0. What is y?
0, 1
Let a = 1106 + -1106. Suppose -2*k + 57 - 49 = a. Determine i, given that 20/13 - 158/13*i**3 + 30/13*i**k + 22/13*i**2 + 86/13*i = 0.
-2/5, -1/3, 1, 5
Let j = -650 + -295. Let o be (-12)/(-14) + 180/j. Suppose o - 23/6*w**3 + 11/6*w**2 + 10/3*w - 2*w**4 = 0. Calculate w.
-2, -2/3, -1/4, 1
Factor -2/15*y**2 - 8/3*y + 88/15.
-2*(y - 2)*(y + 22)/15
Suppose 370*y - 483 = 347*y. Let i(c) be the first derivative of -5*c**2 + 14/3*c**3 - 4*c - y. Let i(l) = 0. Calculate l.
-2/7, 1
Suppose -5*o + 3*h + 210 = -o, -o + 48 = -3*h. Find n, given that -39*n**2 + 12*n**4 + 46*n**5 + 85*n**3 + o + 29*n**3 - 70*n**5 - 117*n = 0.
-3/2, 1/2, 1, 2
Let d(b) be the second derivative of b**5/100 + 4*b**4/15 + 73*b**3/30 + 9*b**2 - 1407*b. Factor d(g).
(g + 2)*(g + 5)*(g + 9)/5
Let g(n) = -n**3 + 11*n**2 - 14*n - 32. Let s be (162/(-4))/(-3)*46/69. Let q be g(s). Suppose -q - 5/2*w**4 - 6*w + 3/2*w**3 + 11*w**2 = 0. What is w?
-2, -2/5, 1, 2
Let t(j) be the second derivative of -j**7/42 + 5*j**6/3 + 26*j - 21. Find p such that t(p) = 0.
0, 50
Let j = -49 - -62. Suppose j*k = 9*k + 48. Solve 3*m + k*m - 15*m + 4*m**2 + 8*m = 0.
-2, 0
Solve 2/5*d**4 + 1568 - 9968/5*d + 450*d**2 - 124/5*d**3 = 0.
1, 5, 28
Let y be (1920/(-3168))/((-45)/132). Find c such that y*c**2 - 4/9*c**4 + 16/3*c + 0 - 4/3*c**3 = 0.
-3, -2, 0, 2
Let a(j) be the third derivative of j**8/168 - 6*j**7/35 + 7*j**6/5 - 77*j**5/15 + 41*j**4/4 - 12*j**3 + 67*j**2 - 3*j - 1. Factor a(u).
2*(u - 12)*(u - 3)*(u - 1)**3
Let d(b) = -8*b - 126. Suppose 65 = -5*x - 5*l, -5*l = 5*x - x + 49. Let j be d(x). Let -16/21*y - 2/7*y**3 - 22/21*y**j + 8/21 = 0. What is y?
-2, 1/3
Let u = 1402356/65 + -280440/13. Determine j so that -3*j**3 - 9/5*j**2 + 3*j + u - 3/5*j**4 = 0.
-4, -1, 1
Determine z so that 100*z**2 - 89*z - z**3 + 183 - 253 - 120*z**2 = 0.
-14, -5, -1
Let f(h) = 32*h**5 - 276*h**4 - 1506*h**3 + 276*h**2 + 1510*h - 2. Let r(b) = 18*b**5 + b**3 - b - 1. Let i(y) = f(y) - 2*r(y). Solve i(k) = 0 for k.
-63, -6, -1, 0, 1
Let z(p) be the third derivative of -p**2 + 1/315*p**7 + 0*p + 1/18*p**4 - 1/90*p**6 + 1/3*p**3 - 12 - 2/45*p**5. Let z(u) = 0. What is u?
-1, 1, 3
Let a(v) be the third derivative of -5*v**8/336 + 2*v**7/7 - 17*v**6/24 - 17*v**5/6 + 15*v**4/2 + 100*v**3/3 - 19*v**2 - 29. Suppose a(k) = 0. Calculate k.
-1, 2, 10
Let m(t) be the first derivative of -3/7*t**2 + 0*t + 165 + 20/21*t**3 - 3/14*t**4. Suppose m(y) = 0. What is y?
0, 1/3, 3
Let t = -290/719 + 15250/2157. Factor 0 - 5/3*l**2 - t*l.
-