-20/3*u**2 + 10/3*u**3 - 4/3 + 0*u**4 - 1/3*u**5 + 5*u.
-(u - 1)**4*(u + 4)/3
Let i = -3192/5 - -12773/20. Let r(w) be the second derivative of 1/8*w**4 - 3/40*w**5 + i*w**3 - 3/4*w**2 + 4*w + 0. Find k such that r(k) = 0.
-1, 1
Let n(c) be the first derivative of c**5/30 + 37*c**4/6 + 1369*c**3/3 + 130*c**2 - 98. Let s(z) be the second derivative of n(z). Factor s(m).
2*(m + 37)**2
Let a(b) be the second derivative of b**5/10 + 23*b**4/6 - 36*b**3 + b + 407. Factor a(i).
2*i*(i - 4)*(i + 27)
Let w = 447 - 471. Let c be ((-160)/w - 7) + 169/12. Let 45/4*x**2 - 5/4*x**3 + 5 - 5/4*x**4 - c*x = 0. What is x?
-4, 1
Find c, given that -2/7*c**4 - 122/7*c**2 - 32/7*c**3 - 132/7*c + 0 = 0.
-11, -3, -2, 0
Let u be 143/14 - (-796)/2786. Factor 3/2*a**3 - 27/2*a**2 - u + 45/2*a.
3*(a - 7)*(a - 1)**2/2
Let x = -3114991/6 - -519186. Factor 5/6*b**5 - 35/6*b**4 + 95/6*b**3 + 40/3*b - x*b**2 - 10/3.
5*(b - 2)**2*(b - 1)**3/6
Let x(c) be the second derivative of -c**7/49 - 11*c**6/105 + c**5/10 + 47*c**4/42 + 20*c**3/21 - 12*c**2/7 - 1446*c - 1. Suppose x(n) = 0. What is n?
-3, -2, -1, 1/3, 2
Let u = 365075/2 + -182482. Let -u*o**3 + 111/2*o**4 - 87/2*o**2 - 12 - 6*o**5 + 123/2*o = 0. Calculate o.
-1, 1/4, 1, 8
Suppose 30930 = 97*z - 19995. Let m = z + -525. Determine l so that m - 2/13*l**3 + 4/13*l - 2/13*l**2 = 0.
-2, 0, 1
Let x(k) be the first derivative of 1/48*k**4 + 1/90*k**5 + k**2 - 1/720*k**6 + 0*k - 3 - 1/2*k**3. Let q(i) be the second derivative of x(i). Factor q(p).
-(p - 3)**2*(p + 2)/6
Let m(b) be the first derivative of -3*b**4/20 - 38*b**3/5 - 279*b**2/2 - 1080*b + 1273. Factor m(r).
-3*(r + 8)*(r + 15)**2/5
Let q = 341/43 - 851/129. Suppose x - t = 5, 4*x + 0*t + 3*t = -1. Suppose -q*f**x + 8/3 + 4/3*f = 0. Calculate f.
-1, 2
Suppose 0 = -8*f + 685 - 645. Suppose 4*c**f + 5*c + 10228*c**3 - 10236*c**3 - c = 0. What is c?
-1, 0, 1
Let g(q) = 25*q**2 + 918*q + 212521. Let y(v) = -6*v**2 + v. Let n(u) = 3*g(u) + 12*y(u). Solve n(l) = 0.
-461
Let g be 770/(-330) - 28/(-12). Let v(m) be the first derivative of -2 + 0*m - 2/33*m**3 + g*m**2. Factor v(o).
-2*o**2/11
Suppose -142*c = -143*c + 6. Let w be c/(-8) + (-123)/(-164). Determine a so that 2/11*a**2 + w - 6/11*a = 0.
0, 3
Let g = -730 + 732. Factor -3*m**4 + 105 + 96*m**2 + 51*m + 18*m**g + 165*m.
-3*(m - 7)*(m + 1)**2*(m + 5)
Suppose -u + 5*u + 2872 = 5*v, -2*v + 2*u + 1150 = 0. Suppose -5*m + 568 = -v. Factor 17*w**3 - 128*w**2 + 5*w**3 - 2*w**3 - 72 + m*w.
4*(w - 3)**2*(5*w - 2)
Suppose -4*t + 57*x = 55*x - 26, 23 = -4*t - 5*x. What is d in -6 + 9*d - 10/3*d**2 + 1/3*d**t = 0?
1, 3, 6
Factor -3*w**4 + 0*w**4 - 3*w + 0*w**2 - 25*w**3 + 3*w**2 - 25*w**3 + 53*w**3.
-3*w*(w - 1)**2*(w + 1)
Let c(q) = -75*q + 5786. Let w be c(77). Let g(p) be the third derivative of -1/150*p**5 + 0 + 0*p + w*p**2 + 1/30*p**4 + 0*p**3. Suppose g(i) = 0. What is i?
0, 2
Let t(z) = -z**2 - 27*z - 45. Let g be t(-25). Let p be -3*(-8)/(-16)*g/(-3). Let 1/2*q**3 + 0 + p*q + 3*q**2 = 0. What is q?
-5, -1, 0
Factor -12*c**2 + 63*c + 1199 + 437*c + 4*c**3 - 26*c**2 - 474*c**2 - 183.
4*(c - 127)*(c - 2)*(c + 1)
Let h be 968/(-2064) + 2/4. Let l = 203/387 + h. Factor 4/9*n**3 + 2/9*n + l*n**2 + 1/9*n**4 + 0.
n*(n + 1)**2*(n + 2)/9
Suppose l - 62 = -43. Suppose -l*f + 97 = 40. Find h, given that -10/13*h - 2/13*h**f - 4/13*h**4 + 16/13*h**2 + 0 = 0.
-5/2, 0, 1
Let u(n) = 5*n**3 + 1070*n**2 + 40*n - 40. Let l(f) = -f + 1. Let i(w) = -40*l(w) - u(w). Determine x, given that i(x) = 0.
-214, 0
Find j such that -250/3*j + 2/3*j**3 - 244/3*j**2 + 164 = 0.
-2, 1, 123
Let w(d) be the second derivative of -d**7/14 - 3*d**6/5 - 6*d**5/5 + 4*d**4 + 24*d**3 + 48*d**2 - 790*d. Factor w(j).
-3*(j - 2)*(j + 2)**4
Find y, given that -6/7*y**3 - 2*y**2 + 16*y - 120/7 = 0.
-6, 5/3, 2
Let o = -206 + 619/3. Suppose 8 = 14*m - 20. Factor -m*p + o*p**2 - 7/3.
(p - 7)*(p + 1)/3
Factor 553536 + 2976*c - 20757*c**2 + 10370*c**2 + 10391*c**2.
4*(c + 372)**2
Let y(c) = -c**3 + c**2 - c + 29. Let f be y(0). Let s be f/(-58) - 1/(1 + -2). What is n in 1/2*n**2 - 1/4*n**5 - 1/4 - 1/4*n + s*n**3 - 1/4*n**4 = 0?
-1, 1
Let h(j) be the first derivative of -j**4/7 + 1864*j**3/7 - 1302936*j**2/7 + 404778784*j/7 - 2535. What is n in h(n) = 0?
466
Factor -121801/5 - 1/5*k**2 + 698/5*k.
-(k - 349)**2/5
Let k be (-528)/(-384)*-64 + 90. Solve 1/2*t**k + 1058 + 46*t = 0.
-46
Let h(j) be the second derivative of 3*j**5/160 + 1473*j**4/32 + 723243*j**3/16 + 355112313*j**2/16 + 17*j - 15. Factor h(u).
3*(u + 491)**3/8
Let f(r) = -3*r + 1. Let p(b) = -5*b + 243. Let z(t) = -6*f(t) + p(t). Let d be z(-18). Solve 2/3*o**d - 2/3*o + 0 + 0*o**2 = 0 for o.
-1, 0, 1
Let k = -90 + 118. Suppose -26*p + k*p = 0. Factor p + 2/3*h**4 + 4/3*h - 2/3*h**2 - 4/3*h**3.
2*h*(h - 2)*(h - 1)*(h + 1)/3
Let y(w) be the third derivative of -w**5/270 - 11*w**4/54 + 16*w**3/9 - 24*w**2 - 4*w. Find n such that y(n) = 0.
-24, 2
Let u(q) be the third derivative of -q**7/75 - 11*q**6/300 + q**5/50 + 11*q**4/60 + 4*q**3/15 - 1284*q**2. Suppose u(o) = 0. Calculate o.
-1, -4/7, 1
Let m(n) be the first derivative of 18/11*n**2 + 56 + 2/33*n**3 + 162/11*n. Factor m(t).
2*(t + 9)**2/11
Factor 20*l**3 - 133*l**2 + 137*l**2 - 23*l**3.
-l**2*(3*l - 4)
Let s(q) = 156*q**2 - 1992*q + 6062. Let i(a) = 311*a**2 - 3986*a + 12126. Let o(f) = -6*i(f) + 13*s(f). Solve o(y) = 0.
55/9
Let m(n) be the third derivative of 3*n**7/280 + 17*n**6/240 - 107*n**5/240 + 19*n**4/24 - n**3/2 + 177*n**2. Factor m(d).
(d - 1)**2*(d + 6)*(9*d - 2)/4
Suppose -2*v + 88 = -4*i, -v - 7*i = -3*i - 32. Determine r so that -28*r**2 - 2 + v*r - 61 + 63 + 4*r**3 = 0.
0, 2, 5
What is j in -202*j + 36*j**3 + 375*j - 40*j**3 - j**2 + 47*j + 152 + 65*j**2 = 0?
-2, -1, 19
Let p(g) = 39*g**2 - 20*g - 72. Let m be p(-4). Suppose -m*j = -621*j. Factor 3/8*k**5 - 3/8*k**3 + 0*k**2 + 0*k**4 + 0 + j*k.
3*k**3*(k - 1)*(k + 1)/8
Let q(s) = -4*s - 81. Let k be q(-20). Let r be ((-2)/k)/(24 - 16) + 0. Factor -r + 1/4*m**3 - 1/4*m + 1/4*m**2.
(m - 1)*(m + 1)**2/4
Let d be 10/(7 + -9) + (-6717)/(-6). Let t = d + -1114. Find c, given that 0*c + 0*c**3 + t*c**2 + 0 - 1/2*c**4 = 0.
-1, 0, 1
Let 1/5*d**5 + 0*d - 17/5*d**4 + 0 + 11*d**3 - 39/5*d**2 = 0. What is d?
0, 1, 3, 13
Let s be ((-15)/(-36)*-8)/((-4)/(-6)). Let o be s + ((-321)/(-60) - 1/(-4)). Factor -2/5 + o*a - 1/5*a**2.
-(a - 2)*(a - 1)/5
Let y(l) = 7*l**2 - 22*l + 165. Let o(c) = 8*c**2 + 8*c + 164. Let s(b) = -5*o(b) + 6*y(b). Factor s(d).
2*(d - 85)*(d - 1)
Suppose c - 4*s + 22 = 0, -c - 95*s + 91*s = -26. Let g(t) be the second derivative of t**c - 1/8*t**4 - 1/40*t**5 - 14*t + 0 + 0*t**3. Let g(i) = 0. What is i?
-2, 1
Let f = -47079/40 + 1177. Let t(i) be the third derivative of 0*i + 0*i**4 + f*i**6 + 1/90*i**5 + 1/90*i**7 - 7*i**2 + 0*i**3 + 0. What is v in t(v) = 0?
-1, -2/7, 0
Let v(n) = 3*n**2 + 183*n + 54. Let x(r) = r + 6. Let t(l) = v(l) - 9*x(l). Factor t(u).
3*u*(u + 58)
Suppose -4*d + 4 = 2*c - 14, 0 = 5*d + 4*c - 30. Factor -29*y + 2*y**2 - 25*y**d + 22*y**2.
-y*(y + 29)
Let u = -207 - -744. Let w = u - 534. Solve 2*x - w*x**2 - 1/3 = 0 for x.
1/3
Let l be (-15210)/16380*14/(-5). What is i in -1/5*i**5 + 9/5 - 42/5*i**3 + 58/5*i**2 + l*i**4 - 37/5*i = 0?
1, 9
Let b be (-9)/(-12) - (-25)/(-500)*-195. Factor b*u + 45/2 - 21/2*u**2 + 3/2*u**3.
3*(u - 5)*(u - 3)*(u + 1)/2
Let o = -931/2458 + 1080/1229. Determine n so that -1/2 + 1/2*n**4 + 7/4*n + o*n**3 - 1/4*n**5 - 2*n**2 = 0.
-2, 1
Suppose -1002001/3 - 2002/3*g - 1/3*g**2 = 0. What is g?
-1001
Let a(i) be the second derivative of i**7/210 + i**6/10 - 18*i**4 + 105*i**3/2 + 34*i + 1. Let x(j) be the second derivative of a(j). Find h such that x(h) = 0.
-6, 3
Let n be (-6)/8 - (287/28 - 11). Let k be ((-408)/2652)/(n + 2/(-26)). Solve 1/8*p**3 - 7/8*p**4 + 0*p**k + 0 + 0*p + 3/2*p**5 = 0.
0, 1/4, 1/3
Suppose 45*z + 15 = 50*z. Factor v**z + 100 + 81*v - 3*v + 2*v - 19*v**2.
(v - 10)**2*(v + 1)
Suppose -j - 4*c = 32, 2*j + 5*c - 32 = -72. Let m(w) be the second derivative of j + 1/9*w**4 + 4/9*w**3 - 1/15*w**5 + 0*w**2 - 28*w. Factor m(x).
-4*x*(x - 2)*(x + 1)/3
Let b(r) = 2*r**3 + r**2 - 15*r - 3. Let q(w) = 68 - 31*w + 3*w**3 - 73 + 2*w + w**2 + w**3. Let v(m) = -5*b(m) + 3*q(m). Determine u, given that v(u) = 0.
-2, 0, 3
Le