 m + 10507/3702. What is p in -14/3*p**2 - 4/3*p**4 + 1/6*p**5 + g*p + 11/3*p**3 - 2/3 = 0?
1, 4
Suppose 3*a - 2*i = -1, -a + 4*i - 9 = -2. Let h be (-8 + -1 - -12) + 1/a. Factor h*m**3 - 9/2*m**5 + 0 - 2*m**2 + 0*m + 3/2*m**4.
-m**2*(m + 1)*(3*m - 2)**2/2
Factor -q**3 + 198 + 48*q**2 - 187*q**2 - 126*q + 69*q**2 - q**3.
-2*(q - 1)*(q + 3)*(q + 33)
Let l(o) be the second derivative of o**4/6 + 1346*o**3/3 + 452929*o**2 + 250*o + 2. Determine j, given that l(j) = 0.
-673
Find q such that -3/4*q**2 + 0*q + 108 = 0.
-12, 12
Let j(c) = -c**3 + 516*c**2 + 533*c. Let o(r) = -4*r**3 + 1549*r**2 + 1597*r. Let b(z) = -11*j(z) + 4*o(z). Let b(n) = 0. Calculate n.
-1, 0, 105
Let s = -18/227 - -1999/10896. Let d(h) be the third derivative of -25/24*h**3 + 0*h + 0 + s*h**4 - 1/240*h**5 + 17*h**2. Factor d(z).
-(z - 5)**2/4
Let s be 30/(-24)*(-36)/15. Let x(w) be the first derivative of w**6 - 15/2*w**5 + 21*w**2 + 87/4*w**4 - 6*w - 61/2*w**s - 7. Determine h, given that x(h) = 0.
1/4, 1, 2
Let w(h) be the first derivative of -2*h**3/45 + 44*h**2/5 - 104*h/3 - 5880. Solve w(u) = 0 for u.
2, 130
Solve -261*a**4 - 1821*a**3 + 176*a**2 + 3620*a**3 - 30*a - 32*a**2 + 27*a**5 - 1904*a**3 + 9*a**2 = 0 for a.
-1, 0, 1/3, 10
Find n such that 4*n**2 + 6*n**2 - n**4 + 528*n**3 - n**5 + 3*n**2 - 1050*n**3 + 6*n + 529*n**3 = 0.
-2, -1, 0, 3
Find w such that -20304/7*w**2 - 34445979648/7 - 45805824/7*w - 3/7*w**3 = 0.
-2256
Let w be (-200)/(-45)*5*(-30)/(-125). Let z = -33/10 + 259/30. Find u such that -z*u + w + 4/3*u**2 = 0.
2
Let r(j) be the first derivative of 0*j + 3/13*j**2 + 2/65*j**5 - 3/26*j**4 - 2/39*j**3 + 74. Factor r(m).
2*m*(m - 3)*(m - 1)*(m + 1)/13
Suppose 5*y + 192*v = 199*v - 11, 2*y + 5*v = 19. Suppose -32/11 - 6*o - 2/11*o**3 - 36/11*o**y = 0. What is o?
-16, -1
Let f(g) be the third derivative of g**9/120960 - g**7/2520 + 17*g**5/60 + g**4/12 - 26*g**2 + 1. Let l(q) be the third derivative of f(q). Solve l(k) = 0.
-2, 0, 2
Let c = -10/8349 - -400802/41745. Solve c*k - 56/5*k**2 + 32 - 12/5*k**3 + 4/5*k**4 = 0.
-2, 2, 5
Let z = 237913/21 - 33985/3. Let n be 0 - (-8)/(-14)*-1. Solve -12/7*c - n + 43/7*c**2 - 45/7*c**4 + z*c**3 = 0.
-1, -1/5, 2/3
Suppose 5*t + 14*s - 56 = 0, 0*t = -2*t + 3*s - 12. Let x = -89/3 + 30. Factor -x*n**3 + t + 0*n + 1/3*n**2.
-n**2*(n - 1)/3
Factor 608 + 614 - 1798 + 608 - 66*w + 4*w**2.
2*(w - 16)*(2*w - 1)
Let c(f) be the first derivative of -f**3/3 - 11*f**2/2 + 26*f - 1385. Factor c(j).
-(j - 2)*(j + 13)
Let t(y) be the third derivative of -y**6/540 + 97*y**5/90 - 32*y**4/3 + 1148*y**3/27 - 2*y**2 + 782*y. Solve t(j) = 0.
2, 287
Let q = -10295 + 10300. Let m(b) be the second derivative of 0 + 1/26*b**4 + 0*b**3 - 1/130*b**q - 4/13*b**2 + 2*b. Factor m(u).
-2*(u - 2)**2*(u + 1)/13
Factor 18 - 1/6*k**2 + 2*k.
-(k - 18)*(k + 6)/6
Suppose 0 = 4*d - 2*b - 728, -5*d + 3*b = -10*d + 932. Factor -31*h**2 + d*h**2 - 497*h**3 + 14739 + 500*h**3 + 2601*h.
3*(h + 17)**3
Let g(q) be the first derivative of -25*q**6/6 + 18*q**5 + 10*q**4 + 284. Factor g(x).
-5*x**3*(x - 4)*(5*x + 2)
Let g(s) be the second derivative of -s**4/4 + 2*s**3 + 135*s**2/2 - 315*s - 2. Factor g(n).
-3*(n - 9)*(n + 5)
Let f(v) be the first derivative of v**3/6 + 28*v**2 + 327*v/2 + 4356. Factor f(r).
(r + 3)*(r + 109)/2
Suppose -8*x = 33*g - 30*g, -4*x + 2*g + 28 = 0. Factor -1/5 - 112/5*r**3 - 72/5*r**2 - x*r.
-(4*r + 1)**2*(7*r + 1)/5
Let b(f) be the first derivative of -152 - 1/9*f**3 - 256/3*f - 16/3*f**2. Factor b(r).
-(r + 16)**2/3
Let u be (2/24)/((-35)/(-14) + 7 - 9). Solve 0 + u*p**4 + 0*p + 1/2*p**3 + 1/3*p**2 = 0 for p.
-2, -1, 0
Let q be (7106/(-132) - -55) + ((-1)/2)/1. Determine z so that 0 - 1/3*z**3 + 1/3*z**4 - q*z**2 + 0*z = 0.
-1, 0, 2
Suppose 8 = 27*y - 25*y. Factor -17*w - 26*w - 24 + y*w**3 + 15*w.
4*(w - 3)*(w + 1)*(w + 2)
Let w = -2111/15 - -2327/15. Find i, given that 9*i**2 + 12/5*i**3 + 3 - w*i = 0.
-5, 1/4, 1
Factor -1033*s**2 + 2046*s**2 + 564*s - 1022*s**2 - 915.
-3*(s - 61)*(3*s - 5)
Let o = -18805 + 376101/20. Let f(t) be the first derivative of 1/6*t**3 - 1/4*t + 0*t**2 + 33 - o*t**5 + 0*t**4. Factor f(m).
-(m - 1)**2*(m + 1)**2/4
Suppose -o + y = -6, 2*o = -0*o + y + 8. Let i be 3 + 1 + o + 4 + -8. Factor 12*m**i - 102*m - 16 + 4*m**3 + 102*m.
4*(m - 1)*(m + 2)**2
Let k(l) be the first derivative of -l**4/2 + 134*l**3/15 - 26*l**2/5 - 8180. Factor k(a).
-2*a*(a - 13)*(5*a - 2)/5
Let c(t) be the third derivative of -t**6/6 + 2*t**5 - 75*t**4/8 + 125*t**3/6 + 29*t**2 - 4. What is a in c(a) = 0?
1, 5/2
Let n(j) = 14*j**2 + 824*j - 120. Let z(b) = 14*b**2 - 2*b - 1. Let t(c) = 2*n(c) - 4*z(c). Factor t(m).
-4*(m - 59)*(7*m - 1)
Let u = -124377 - -124377. Determine z, given that -2/15*z**4 + 0 + 2/15*z**5 - 4/15*z**3 + u*z + 0*z**2 = 0.
-1, 0, 2
Let f be -5*(-11)/55*2. Let i(t) be the second derivative of 0*t**f + 0 - 1/16*t**4 - 1/4*t**3 + 14*t. Factor i(w).
-3*w*(w + 2)/4
Suppose -54 - 40*o**3 + 81/2*o - 1/2*o**5 + 9*o**4 + 45*o**2 = 0. What is o?
-1, 1, 3, 12
Suppose -2*i - 2*b = -0*b - 26, -i = -5*b - 7. Let j(r) be the first derivative of 4*r + 4/5*r**5 - 8/3*r**3 + 2/3*r**6 + i + 2*r**2 - 2*r**4. Factor j(k).
4*(k - 1)**2*(k + 1)**3
Let p(n) be the first derivative of -1/38*n**4 + 0*n - 42 - 7/19*n**2 - 16/57*n**3. Factor p(v).
-2*v*(v + 1)*(v + 7)/19
Let l(j) be the third derivative of -j**2 - 2 - 1/480*j**6 - 1/48*j**4 - 1/80*j**5 + 0*j + 0*j**3. Find h, given that l(h) = 0.
-2, -1, 0
Let q(y) = -y**3 - 320*y**2 - 23716*y - 8. Let m(u) = -u**3 - 317*u**2 - 23716*u - 6. Let v(n) = -4*m(n) + 3*q(n). Solve v(t) = 0 for t.
-154, 0
Let w(h) = -10*h - 114. Let z be w(-11). Let i be z/((-328)/123 - (-4)/6). Determine c so that -2/7 + 4/7*c - 2/7*c**i = 0.
1
Let n(o) be the first derivative of o**6/20 + 3*o**5/8 + o**4 + o**3 + 167*o - 43. Let r(b) be the first derivative of n(b). Determine i so that r(i) = 0.
-2, -1, 0
Let o = -75955/21 + 3617. Let u(t) be the first derivative of 6 - 22/35*t**5 - 4/7*t**2 - o*t**6 - 3/2*t**4 - 32/21*t**3 + 0*t. Determine j so that u(j) = 0.
-2, -1, -1/2, 0
Let l be (4/(-6))/((-20)/1470) - -5. What is g in 10*g + 19*g + 49*g**2 - l*g**2 - 4*g = 0?
0, 5
Let u(d) = -2*d**4 - 38*d**3 + 140*d**2 - 162*d + 64. Let r(w) = 2*w**4 - w**3 - w**2 - w. Let m(q) = -2*r(q) - u(q). Let m(b) = 0. What is b?
1, 2, 16
Let p be 21/((-1134)/(-12)) + 16/(-180). Let b = 128 - 128. Let -4/15*r**5 + 4/5*r**3 + p*r**4 - 14/15*r**2 + b + 4/15*r = 0. Calculate r.
-2, 0, 1/2, 1
Determine x, given that 105/4*x + 3/4*x**2 - 27 = 0.
-36, 1
Let z(b) = b**3 - 6*b - 5. Let t(o) = 2*o**2 - 4*o - 1. Let h be t(0). Let u be z(h). Factor -c**3 + 3/2*c**4 + 0*c - 1/2*c**5 + u + 0*c**2.
-c**3*(c - 2)*(c - 1)/2
Let n(m) be the second derivative of 7*m**4/12 - 3170*m**3/3 - 906*m**2 + 1417*m + 2. What is o in n(o) = 0?
-2/7, 906
Suppose -75 = -338*w + 335*w + 5*r, 45 = 4*w - 3*r. Find f, given that 1/6*f**4 + 1/3*f**3 + w*f + 0 - 1/2*f**2 = 0.
-3, 0, 1
Factor 3/8*t**2 + 45/8 + 3*t.
3*(t + 3)*(t + 5)/8
Suppose 0 = 2*q + q + 3, 34 = 5*d + q. What is x in -5*x**5 - 8 + 16*x**3 - 2*x + 2*x**2 + 27*x**3 + d*x**4 + 35*x**2 = 0?
-1, 2/5, 4
Let p be -3 + (0/(-1) - -2238). Factor -p*x**2 - 37 + 2184*x**2 - 111*x - 20 + 3*x**3.
3*(x - 19)*(x + 1)**2
Factor 155/2*m - 78 + 1/2*m**2.
(m - 1)*(m + 156)/2
Let f(h) be the third derivative of h**5/20 + 23*h**4/4 + h**2 + 296. Solve f(v) = 0.
-46, 0
Let x(o) be the second derivative of o**4/21 - 1268*o**3/21 - 1270*o**2/7 - 3*o + 130. Solve x(v) = 0.
-1, 635
Solve -2120*f**2 + 128*f + 2376*f**2 + 32*f**4 + 4*f**5 + 168*f**3 + 9*f**4 + 3*f**4 = 0 for f.
-4, -2, -1, 0
Factor -845*b + 595*b + 454*b - 3*b**2 - 1116.
-3*(b - 62)*(b - 6)
Find y, given that 2/13*y - 60/13 + 62/13*y**2 = 0.
-1, 30/31
Let y(w) be the first derivative of -2*w**6/15 - 28*w**5/25 + 18*w**4/5 - 8*w**3/15 - 34*w**2/5 + 36*w/5 + 24. Suppose y(f) = 0. Calculate f.
-9, -1, 1
Let m = 407472 - 407468. Factor 2/15 + 2/15*f**m + 0*f - 4/15*f**2 + 0*f**3.
2*(f - 1)**2*(f + 1)**2/15
Let l(w) = 60*w**3 - 305*w**2 + 1400*w - 1645. Let a(i) = 71*i**3 - 306*i**2 + 1399*i - 1644. Let k(j) = 5*a(j) - 6*l(j). Find y, given that k(y) = 0.
2, 3, 55
Let v(j) be the first derivative of 636/11*j**2 + 160/11*j + 1112/11*j**3 + 60 + 1415/22*j**4 - 30/11*