8354/5. Let m = n + 538. Suppose 2/5*p**3 + 0 - m*p**2 + 0*p = 0. Calculate p.
0, 2
Let k(j) be the third derivative of j**7/210 + j**6/120 - j**5/10 - j**4/6 + 4*j**3/3 - 4*j**2 + 499*j. Factor k(f).
(f - 2)*(f - 1)*(f + 2)**2
Suppose -4*l = -5*t + 2, 4*l = 3*t + t. Suppose 4946*x - 6512 - 3865 - 3078 = -3563. Factor -l*d**x - 1/3*d**3 - d + 10/3.
-(d - 1)*(d + 2)*(d + 5)/3
Let t(j) be the third derivative of -j**5/60 + 182*j**4/3 - 264992*j**3/3 - 489*j**2. Determine q so that t(q) = 0.
728
Let w(h) = -8*h - 7. Let u be w(-5). Factor 2*c**2 + 1146 + 82*c + u*c + 902 + 13*c.
2*(c + 32)**2
Let o(y) be the first derivative of 1587/7*y + 69/7*y**2 + 1/7*y**3 - 35. Factor o(p).
3*(p + 23)**2/7
Suppose 3*x - x - 6 = 0. Let t = -10243/120 + 2063/24. Find h, given that 12/5 + 12/5*h - t*h**2 - 3/5*h**x = 0.
-2, -1, 2
Let t(j) be the first derivative of 35*j**6/18 - 10*j**5 + 5*j**4/12 + 50*j**3/3 - 20*j**2/3 - 792. Determine a, given that t(a) = 0.
-1, 0, 2/7, 1, 4
Suppose 6*p - 7 = p + 2*w, -2*p + 2*w - 2 = 0. Let m be (-2)/(-4) + 390/60 + -6. What is q in -m + 1/2*q**p - 11/2*q - 6*q**2 + 2*q**4 = 0?
-1, -1/4, 2
Let u(s) be the second derivative of s**6/90 + 7*s**5/60 - s**4/12 - 23*s**3/18 - 7*s**2/3 - 216*s. Determine q, given that u(q) = 0.
-7, -1, 2
Let m be (-890)/8811*(-68)/(-10). Let t = -2/99 - m. Factor 4/9*s**5 + 0*s**2 + 2/9*s**3 + 0 + 0*s - t*s**4.
2*s**3*(s - 1)*(2*s - 1)/9
Suppose -9*s + 5*s + 20 = 0. Solve -15*p + 7*p - 40*p**3 + 50*p**3 - 2*p**s = 0 for p.
-2, -1, 0, 1, 2
Find u such that 56*u**4 + 806*u**4 - 156*u**4 - u**5 + 1020*u**3 + 508*u**2 - 190*u**4 + 5*u**5 = 0.
-127, -1, 0
Factor -4805*x + 6*x**2 - 149175 + 622483 + 214897 + 1095*x - x**2.
5*(x - 371)**2
Let o(s) be the third derivative of 0 + 0*s - 1/90*s**5 - 15*s**2 + 0*s**3 - 1/720*s**6 + 0*s**4. Determine p, given that o(p) = 0.
-4, 0
Let w(i) be the second derivative of -1/120*i**5 - 10*i - 1/6*i**3 + 0*i**2 - 7/72*i**4 - 4. Suppose w(o) = 0. Calculate o.
-6, -1, 0
Let d(l) = -4*l + 60. Let m be d(15). Suppose -86*t + 46*t = m. Factor 0*k**3 + 3/4*k**2 - 3/8*k**4 - 3/8 + t*k.
-3*(k - 1)**2*(k + 1)**2/8
Let u(p) be the third derivative of p**8/5040 - p**7/280 + p**6/90 + p**5/6 - 15*p**2 + p. Let k(n) be the third derivative of u(n). Factor k(s).
2*(s - 4)*(2*s - 1)
Let h(n) be the second derivative of -n**5/30 + 115*n**4/36 - 127*n**3/6 + 27*n**2 - n - 4229. Factor h(t).
-(t - 54)*(t - 3)*(2*t - 1)/3
Let c be (-13)/(-5) + (-3835)/1475. Factor -1/2*w**3 + c*w**2 + 0*w + 0 - w**4.
-w**3*(2*w + 1)/2
Let j(n) be the third derivative of -n**6/40 - 1053*n**5/20 - 276675*n**4/8 + 277729*n**3/2 + n**2 + 985*n + 2. Factor j(o).
-3*(o - 1)*(o + 527)**2
Let o(x) = -3*x - 9. Let i be o(-2). Let f(v) = -v**3 - v**2 - 1. Let c(t) = -2*t**3 - 3*t**2 - 4*t - 3. Let r(s) = i*f(s) + c(s). Determine g so that r(g) = 0.
-2, 0, 2
Let t(w) = -4*w**4 - 694*w**3 - 32230*w**2 - 164654*w + 197552. Let k(f) = -f**3 + f**2 + 7*f + 8. Let b(x) = 2*k(x) + t(x). Factor b(g).
-4*(g - 1)*(g + 7)*(g + 84)**2
What is w in -12/7*w**2 + 536/7*w - 352/7 = 0?
2/3, 44
Let u(p) be the second derivative of p**4/84 - 20*p**3/21 + 200*p**2/7 + 75*p. Solve u(d) = 0.
20
Let t(i) be the third derivative of -13*i**7/420 - i**6/12 - i**5/30 + 43*i**3/6 + 31*i**2. Let k(g) be the first derivative of t(g). Factor k(v).
-2*v*(v + 1)*(13*v + 2)
Let j be 4 - ((-12)/(-30) + (-3)/(-5)). Suppose 6*x + j = 7*x. Factor 2 - 2 - 3*r**3 - 9*r**2 + 9*r**4 + x*r**5.
3*r**2*(r - 1)*(r + 1)*(r + 3)
Factor -1044*n - 31061 + 90896 + 2*n**2 + 76407.
2*(n - 261)**2
Let x(i) = 734*i + 734. Let u be x(-1). Factor u - 66/7*g + 2/7*g**2.
2*g*(g - 33)/7
Let p(t) be the third derivative of -t**7/150 - t**6/300 + 73*t**5/300 - 14*t**4/15 + 8*t**3/5 - 29*t**2 - 1. Let p(h) = 0. What is h?
-4, 1, 12/7
Let h(d) = -18*d**4 - 507*d**3 - 437*d**2 - 65*d - 9. Let l(y) = -18*y**4 - 488*y**3 - 436*y**2 - 64*y - 10. Let f(p) = 20*h(p) - 18*l(p). Factor f(q).
-4*q*(q + 37)*(3*q + 1)**2
Let t(k) = k**3 - 5*k**2 - 19*k - 10. Let r be t(8). Factor -9*u + 3*u**3 - 15*u**2 + 128 + r*u - 137.
3*(u - 3)*(u - 1)**2
Suppose 145*h - 552 = 60*h - 53*h. Let l(q) = -q**3 + 8*q**2 - 5*q + 1. Let c be l(5). Let 4*o**h + 106 + 5*o**3 - 55 + o**2 - c = 0. Calculate o.
-1, -1/4, 0
Let q(m) be the first derivative of m**4/8 - 9*m**3 + 50*m**2 + 4685. Determine y so that q(y) = 0.
0, 4, 50
Let z(q) be the first derivative of -9*q**4/2 + 158*q**3/15 - 39*q**2/5 + 2*q - 2934. Find t, given that z(t) = 0.
1/5, 5/9, 1
Let u be ((-1)/(5/108))/(8/(-40)). Factor -3*z**3 - u*z**2 + 213*z**2 - 93*z**2 + 3*z - 12.
-3*(z - 4)*(z - 1)*(z + 1)
Suppose 61/3*j**3 - 2*j - 181/3*j**2 + 0 = 0. What is j?
-2/61, 0, 3
Let n = 10649/3 - 3548. Let v(d) be the second derivative of 5/6*d**3 + 0 - 1/12*d**5 + 0*d**4 - 9*d - n*d**2. Factor v(c).
-5*(c - 1)**2*(c + 2)/3
Factor -3/5*y**3 - 2016/5 - 30*y**2 - 1056/5*y.
-3*(y + 4)**2*(y + 42)/5
Let u(o) be the second derivative of 0*o**3 - 67/60*o**6 + 0*o**5 + 0*o**2 - 58*o + 0 + 1/84*o**7 + 0*o**4. Factor u(a).
a**4*(a - 67)/2
Let a(n) be the first derivative of 1/3*n**3 - 18*n + 15/4*n**2 - 1/8*n**4 + 17. What is g in a(g) = 0?
-4, 3
Let v(p) be the first derivative of p**5 + 10*p**2 - 55/4*p**4 + 40*p**3 - 91 - 160*p. Determine i, given that v(i) = 0.
-1, 2, 8
Let o be 9*7 + 86346/(-1404). Find d such that 0 + 3/4*d**5 - o*d**4 - 3*d + 6*d**2 - 9/4*d**3 = 0.
-2, 0, 1, 2
Let y = 68 - 66. Let -40 + 12*q - 8*q - 32*q - 4*q**y = 0. Calculate q.
-5, -2
Suppose 182*l + 10245 = 1363*l - 384. Solve l*z - 1/5*z**3 - 21/5*z**2 - 23/5 = 0.
-23, 1
Let c(i) be the first derivative of 2*i**5/45 - 5*i**4/3 - 14*i**3/27 + 24*i**2 - 40*i - 4141. Find h, given that c(h) = 0.
-3, 1, 2, 30
Let f be 42/266 + 69/(-437). Factor f*p + 0 - 3/2*p**4 + 18*p**2 + 3/2*p**5 - 12*p**3.
3*p**2*(p - 2)**2*(p + 3)/2
Suppose -4*h = -5*d + 57 - 110, 2*h + 20 = 18*d. What is p in 268/3*p**d - 104/3*p**5 + 16/3*p - 12*p**4 + 0 - 48*p**2 = 0?
-2, 0, 2/13, 1/2, 1
Let u = 1187 - 397. Factor 10*z - u*z**3 + 791*z**3 - 12*z + z**2.
z*(z - 1)*(z + 2)
Let l(s) be the first derivative of 27 + 32*s**3 + 80*s**2 + 96*s + 2/5*s**5 + 6*s**4. What is m in l(m) = 0?
-6, -2
Let o(r) = 9*r**3 - r**2. Let c be o(1). Let a be (2 - 3 - 3) + c. Let -a*x**3 + 3*x**3 + 31*x**2 - 32*x**2 = 0. Calculate x.
-1, 0
Suppose -k - 6 = -0*k. Let j(u) = 29*u**2 - 29*u. Let d(n) = -10*n**2 + 10*n. Let m = -763 + 746. Let z(p) = k*j(p) + m*d(p). Let z(s) = 0. What is s?
0, 1
Let w be 3*9/54 - (-697)/(-6). Let l = 117 + w. Let 0 + 8/3*m + 4*m**3 - l*m**5 + 4/3*m**4 - 20/3*m**2 = 0. What is m?
-2, 0, 1
Let x = 47 - 43. Let b(d) be the third derivative of 0 - 25/16*d**3 - 1/160*d**5 + 5/32*d**x + 13*d**2 + 0*d. Factor b(c).
-3*(c - 5)**2/8
Let o(i) be the second derivative of -22*i + 6/5*i**5 + 11/30*i**6 - 16*i**3 - 10/3*i**4 - 2 - 8*i**2. Find r, given that o(r) = 0.
-2, -2/11, 2
Let w(a) be the second derivative of -484/9*a**2 - 47/135*a**6 - 1585/54*a**4 + 1496/27*a**3 + 619/90*a**5 + 1/189*a**7 - 1 + 25*a. Factor w(k).
2*(k - 22)**2*(k - 1)**3/9
Let j be 44*((-165)/(-12) + -3) - 0. Let u = 889 - j. What is a in -u*a - 696*a**3 + 36*a**4 - 3760*a - 117*a**2 + 1898*a**2 + 2015*a**2 + 1296 = 0?
2/3, 9
Let p = -14 - -8. Let c be ((-8)/p)/(10/15). Factor -r**2 - 6*r**c - r - 8*r**2 + 19*r**2.
r*(4*r - 1)
Find y, given that 146*y - 475*y + 87*y**2 - 575 - 82*y**2 - 241*y = 0.
-1, 115
Suppose 1005*d**3 - 4201*d**3 - 816*d**2 + 3840*d**4 + 4016*d**2 - 3844*d**4 = 0. Calculate d.
-800, 0, 1
Let z(u) be the first derivative of -u**6/9 + 112*u**5/15 - 1153*u**4/6 + 2404*u**3 - 15732*u**2 + 51984*u + 2993. Solve z(d) = 0 for d.
6, 19
Let g(m) be the second derivative of -m**6/90 + 29*m**5/60 + m**4/36 - 29*m**3/18 - 163*m. Factor g(d).
-d*(d - 29)*(d - 1)*(d + 1)/3
Let 8064/5*w**2 - 16/5*w**3 + 404 + 8076/5*w = 0. Calculate w.
-1/2, 505
Let m(k) be the first derivative of -2*k**3/3 - 3*k**2 + 36*k + 617. What is n in m(n) = 0?
-6, 3
Let b(i) be the first derivative of 5*i**6/6 - 27*i**5 + 235*i**4/4 + 395*i**3/3 - 240*i**2 - 500*i - 1264. Suppose b(k) = 0. Calculate k.
-1, 2, 25
Factor -4*k**3 - 698 - 160*k**2 + 2*k**4 + 698 + 154*k**2.
2*k**2*(k - 3)*(k + 1)
Let v(l) be the first derivative of -l**6/2160 - 7*l**5/240 - 5