*5 + 20/3*n**3. Let i(z) = 0. What is z?
-2, 0, 1
Let o(m) be the third derivative of -m**5/3 + 73*m**4/6 - 84*m**3 + 313*m**2 - m. Suppose o(d) = 0. Calculate d.
2, 63/5
Let 18 - 9/2*y**2 - 3/2*y + 3/8*y**3 = 0. What is y?
-2, 2, 12
Let v be (-3)/(-54)*(-309782)/(-11). Let d = -1563 + v. Find a, given that 4/9*a**2 - 4/9 - d*a + 14/9*a**3 = 0.
-1, -2/7, 1
Let v(f) be the second derivative of -f**5/30 - 203*f**4/18 - 403*f**3/9 - 67*f**2 - 4004*f. Factor v(r).
-2*(r + 1)**2*(r + 201)/3
Let m(o) be the second derivative of o**4/72 + 29*o**3/12 + 21*o**2 - 66*o + 7. Factor m(f).
(f + 3)*(f + 84)/6
Let f(k) = 3*k - 4. Let p be f(3). Suppose -m + 2*d - 6 = -p*m, -4*m - d = -9. Factor -m*q + 2*q - 3*q**5 - 6*q**2 - 4*q + 12*q**3 + 6 - 4*q.
-3*(q - 1)**3*(q + 1)*(q + 2)
Let d = 286 + -775. Let c = d + 1475/3. Factor -40/3*u - c - 50/3*u**2.
-2*(5*u + 2)**2/3
Let r be (-2090)/(-5016) - (-3)/36. Determine z, given that -r*z**3 + 3 + 1/2*z - 3*z**2 = 0.
-6, -1, 1
Factor -2*n**2 - 44*n + 566 + 526 - 182.
-2*(n - 13)*(n + 35)
Let v(r) be the third derivative of 0*r**6 + 1/100*r**5 + 1/60*r**4 + 0 + 0*r - 146*r**2 - 1/1050*r**7 + 0*r**3. Factor v(l).
-l*(l - 2)*(l + 1)**2/5
Let u(z) be the third derivative of -194*z**2 + 0*z - 1/945*z**7 + 0*z**3 + 1/270*z**5 - 1/756*z**8 + 1/270*z**6 + 0*z**4 + 0. What is w in u(w) = 0?
-1, -1/2, 0, 1
Suppose 1 = -b, 5*n - 15 = n - b. Suppose 2*s = -d + 4, n*s - 5*s + 2 = -4*d. Suppose 13*u**2 + 3*u**2 - 7*u + 17*u + 5*u**3 - u**s = 0. Calculate u.
-2, -1, 0
Let y = 80785/12 + -6732. Let c(v) be the third derivative of 0*v - 21*v**2 - 1/90*v**5 - 2/9*v**3 + y*v**4 + 0. Find j such that c(j) = 0.
1, 2
Let v = 281 + -195. Find q such that 22*q**2 - 10 - q**2 - v*q - 2 + 9*q**2 = 0.
-2/15, 3
Let r(z) be the third derivative of -15*z**3 - 1/12*z**5 + 0*z + 0 + 95/24*z**4 + 42*z**2. What is c in r(c) = 0?
1, 18
Let y(d) = -3*d**2 - 56*d - 157. Let n be y(-3). Let j be ((-1575)/126)/(6/n). Factor -1/3*s**2 + 20/3*s - j.
-(s - 10)**2/3
Let j be (-15)/(-35) - (-1160)/70. Suppose 27*v - 88 = -j*v. Factor -2/3*n + 2/3*n**v - 4/3.
2*(n - 2)*(n + 1)/3
Let b = -106 + 109. Factor 2 - 6*k**2 - b + 3*k**3 + 1.
3*k**2*(k - 2)
Let o(x) be the third derivative of 0*x**5 + 3*x**2 + 0*x**4 + 0*x**6 + 9/70*x**7 + 1/112*x**8 + 0*x**3 - 2 + 0*x. Factor o(v).
3*v**4*(v + 9)
Let r(p) be the second derivative of -5365647*p**7 - 15397074*p**6 - 24793839*p**5/2 - 2892460*p**4/3 - 93760*p**3/3 - 512*p**2 + 3721*p. What is o in r(o) = 0?
-1, -8/483
Let d(h) be the first derivative of -h**4/6 + 122*h**3/9 + 397*h**2/3 + 670*h/3 - 3583. Factor d(t).
-2*(t - 67)*(t + 1)*(t + 5)/3
Let r be (-22)/4*(-13 - (-270)/20) + 4. Factor r + n - 1/4*n**2.
-(n - 5)*(n + 1)/4
Let b(t) = t**3 - 24*t**2 + 103*t + 93. Let c be b(18). Factor -1/4*l**4 - 1/2*l**2 + 3/4 + l**c - l.
-(l - 3)*(l - 1)**2*(l + 1)/4
Find a such that -39/8*a**4 - 45/2*a**2 + 0*a + 3/8*a**5 + 39/2*a**3 + 0 = 0.
0, 2, 5, 6
Let h(q) be the second derivative of 2*q**7/105 + 2*q**6 + 217*q**5/25 + 23*q**4/5 - 436*q**3/15 - 288*q**2/5 + 292*q. What is u in h(u) = 0?
-72, -2, -1, 1
Let g(h) be the second derivative of 1/80*h**5 + 2*h + 15 - 1/16*h**4 + 1/120*h**6 + 1/4*h**2 - 1/24*h**3. Factor g(x).
(x - 1)**2*(x + 1)*(x + 2)/4
Let f = 1724 + -1724. Let t(l) be the second derivative of 6*l - 25/3*l**2 - 1/18*l**4 + f + 10/9*l**3. Factor t(m).
-2*(m - 5)**2/3
Let c = -413 + 430. Solve 24*t**3 + 37*t**2 - 22*t**2 + c*t**2 - 12*t**4 - 4*t**5 = 0.
-4, -1, 0, 2
Solve c**3 + c**3 - 81 + 142 + 26*c**2 + 59 + 104*c = 0.
-6, -5, -2
Let r = 99441 + -497204/5. Determine q so that -r*q**2 - 16/5 + 8/5*q = 0.
4
Let l be 72/((-12)/2) - ((-6860)/495 - 18/(-81)). Let k be 0 - 2/(-2) - -1. Factor -8/11*q**3 + 24/11*q - l + 4/11*q**k - 2/11*q**4.
-2*(q - 1)**2*(q + 3)**2/11
Suppose -1196 = 41*f - 18*f. Let a be (-16)/12*(f/8 - -5). Suppose 5/2*j - 11/2*j**a + 2*j**3 + 1 = 0. What is j?
-1/4, 1, 2
Let f(a) be the first derivative of a**4/12 - 130*a**3/9 + 257*a**2/6 - 128*a/3 + 634. Determine m, given that f(m) = 0.
1, 128
Let r(b) be the first derivative of b**5/20 + 21*b**4/16 + 15*b**3/2 - 4*b**2 - 120*b - 6860. Suppose r(f) = 0. Calculate f.
-15, -4, 2
Suppose -2322*j - 1641/4*j**3 - 1377 - 3/4*j**5 - 183/4*j**4 - 5841/4*j**2 = 0. Calculate j.
-51, -3, -2
Let x(t) = 9*t**5 + 24*t**4 + 25*t**3 - 58*t**2 - 10. Let a(d) = -28*d**5 - 72*d**4 - 76*d**3 + 176*d**2 + 32. Let l(c) = 5*a(c) + 16*x(c). Factor l(h).
4*h**2*(h - 1)*(h + 3)*(h + 4)
Let c(q) be the second derivative of -q**4/12 + 79*q**3/6 - 77*q**2 + 1219*q. Factor c(x).
-(x - 77)*(x - 2)
Let a = 16960 + -16960. Let t(o) be the second derivative of 0*o**2 + a + 0*o**3 + 1/10*o**6 + 1/5*o**5 - 1/3*o**4 + 10*o. Factor t(r).
r**2*(r + 2)*(3*r - 2)
Suppose 27 = -6*h + 39. Let -9*m**2 - 410*m**4 - 35*m**3 + 2 - m**2 + 20*m**5 - h + 435*m**4 = 0. Calculate m.
-2, -1/4, 0, 1
Let z be ((-11)/(-55))/(-5 + 2695/1344 + 3). Factor 6/5*j**4 - 66/5*j**3 - z + 24/5*j + 144/5*j**2.
6*(j - 8)*(j - 2)**2*(j + 1)/5
Let z be (-3)/(-25 - 752/(-32)). Solve 540*r**z + 162/5 + 250*r**4 - 600*r**3 - 216*r = 0.
3/5
Determine a, given that 2575*a**3 - 145508*a**2 - 4246*a**4 - 184732*a**2 + 4241*a**4 - 332820*a = 0.
-1, 0, 258
Let l = 42053 + -42049. Solve 34/9*i**2 - 10/3*i**3 - 4/3*i + 0 + 2/9*i**5 + 2/3*i**l = 0.
-6, 0, 1
Let i(p) be the first derivative of p**5/5 - 764*p**4 + 1037342*p**3 - 527487388*p**2 - 1058089859*p - 2851. What is g in i(g) = 0?
-1, 1019
Suppose -3*v + 15 + 26 = -m, -4*m + 16 = 0. What is b in -8*b**3 + 2 - 9 + v*b - 54*b**2 + 14 = 0?
-7, -1/4, 1/2
Let t = -122 + -286. Let x be (t/30 + 4)*(-10)/2. Let 6*y + 27*y**4 + 9*y**2 - x*y**3 - y**2 + 7*y**2 = 0. What is y?
-2/9, 0, 1
Let y be -6 + (19 - 1) + 94/(-8). Find l, given that 19/4*l**4 + 0 + y*l**5 + 81*l**2 + 63/2*l**3 + 54*l = 0.
-6, -1, 0
Let q(x) be the third derivative of x**8/168 + 4*x**7/35 + 7*x**6/12 - 2*x**5/5 - 3*x**4 - 1053*x**2. Solve q(o) = 0.
-6, -1, 0, 1
Let x(m) = 4*m**4 + 4*m**2 + 1. Suppose 5*o - 3*o - 18 = -2*j, 2 = -2*j + 3*o. Let v(r) = -7*r**4 - 6*r**2 - 2. Let t(u) = j*x(u) + 3*v(u). Factor t(c).
-(c - 1)**2*(c + 1)**2
Let m(z) = -4*z**2 - 144*z - 2234. Let i(x) = 7*x**2 + 298*x + 4469. Let a(t) = 6*i(t) + 11*m(t). Let a(j) = 0. Calculate j.
-10, 112
Let b(t) be the second derivative of 0*t**4 + 3/70*t**7 + 1 + 0*t**3 + 3*t - 1/10*t**6 + 3/50*t**5 + 0*t**2. Factor b(u).
3*u**3*(u - 1)*(3*u - 2)/5
Let m(w) be the third derivative of w**7/105 + w**6/10 - 2*w**5/3 - 2*w**4 + 64*w**3/3 + 2070*w**2. Suppose m(o) = 0. Calculate o.
-8, -2, 2
Let 128*k + 87/2*k**2 - 1/4*k**4 + 13/4*k**3 + 88 = 0. What is k?
-4, -1, 22
Let j(n) be the third derivative of -n**8/3360 + n**7/560 - n**6/360 + 71*n**3/6 - 21*n**2 - 2. Let p(x) be the first derivative of j(x). What is d in p(d) = 0?
0, 1, 2
Let m(b) be the first derivative of 0*b**3 - 2/3*b**2 + 0*b - 46 + 1/3*b**4. Let m(u) = 0. Calculate u.
-1, 0, 1
Let t(i) be the second derivative of i**4/20 - 183*i**3/5 + 1092*i**2/5 - 8142*i. Factor t(o).
3*(o - 364)*(o - 2)/5
Suppose -5*q = u + 18, 9 = -5*u - q - 33. Let k be u/(-52) - (3 - (-161)/(-52)). Factor -1/4*h**2 - k + 1/2*h.
-(h - 1)**2/4
Let l(c) = -c**3 - 4*c**2 + 47*c - 9. Let r be l(5). Let f be (14/42)/(r/6). Determine n so that -1/2*n**3 - 3/2*n**f - n + 0 = 0.
-2, -1, 0
Let v(l) be the first derivative of -l**3/3 - 100*l**2 - 199*l - 1762. Determine c, given that v(c) = 0.
-199, -1
Let m = 102 + -96. Let q be (72/90)/(m/(-10) - -1). Factor 24*s + 163*s**2 - 162*s**q + 112 + 32.
(s + 12)**2
Determine m, given that 10/13 - 18/13*m + 2/13*m**3 + 6/13*m**2 = 0.
-5, 1
Let s = 86 + -82. Suppose -4*y - 4*a = 0, -s*y - 2*a = -3*a - 25. Factor 88 - 45 + 2*v - 43 - 5*v**2 - 2*v**3 + y*v**4.
v*(v - 1)*(v + 1)*(5*v - 2)
Let c(d) be the third derivative of -d**7/490 + 9*d**6/70 + 39*d**5/35 + 20*d**4/7 - 294*d**2 + 7*d - 2. Factor c(i).
-3*i*(i - 40)*(i + 2)**2/7
Suppose 0 = y + 5, 3*z + 5*y - 2*y - 288 = 0. Find t such that -36*t**3 - 117*t**4 - 2*t**5 + z*t**4 - 7*t - 3*t - 32*t**2 = 0.
-5, -1, 0
Let a(v) be the third derivative of v**6/160 + 17*v**5/240 - v**4/32 - 17*v**3/24 - v**2 + 199. Factor a(q).
(q - 1)*(q + 1)*(3*q + 17)/4
Suppose 5*b - t = 16, 2*t + 2*t + 4 = 0. Factor 8*i**3 - 2*i**5 - 18*i**b