 - 3)*(i + 1)*(i + 2)/8
Let m(n) be the first derivative of n**6/960 - 9*n**5/160 + 81*n**4/64 + 44*n**3/3 - 58. Let q(z) be the third derivative of m(z). Factor q(y).
3*(y - 9)**2/8
Let d(k) = 3*k**3 - k**2 - k - 12. Let i(r) = 2997*r**4 - 4662*r**3 + 2634*r**2 - 636*r + 240. Let q(c) = -15*d(c) - i(c). What is t in q(t) = 0?
1/3, 20/37
Suppose 3*d + 26 = 5*i - 14, -3*d + 4*i = 35. Let x = 9 + d. Solve 105*z**2 + 2*z + 8*z**3 + 4*z**x - 2*z - 101*z**2 = 0.
-1, 0
Let i = 9572 - 9570. Let k(w) be the second derivative of 3/8*w**4 + 0*w**i - 1/2*w**3 + 0 - 21*w - 3/40*w**5. Suppose k(n) = 0. Calculate n.
0, 1, 2
Let k be (-20)/105*-7 + 46/(-48). Let x = -11/21 + 403/168. Factor -x*l - 3/2 - k*l**2.
-3*(l + 1)*(l + 4)/8
Factor 4172907*n + n**3 - 200 + 4*n**3 + 105*n**2 - 4172817*n.
5*(n - 1)*(n + 2)*(n + 20)
Let c(h) be the third derivative of -h**5/300 + 17*h**4/20 - 20*h**3/3 + 2599*h**2. Find w, given that c(w) = 0.
2, 100
Let d(b) = 2*b + 45. Let s be d(-14). Suppose 18*f = s*f + 16. Find t, given that -2*t**2 - 6*t + 28 - 16 - f = 0.
-2, -1
Let c = 2264219/849081 - 1/283027. Solve 2 + 2/3*o**2 + c*o = 0 for o.
-3, -1
Solve 20*m**4 - 12*m - 265*m**2 - 114*m**2 + 67*m**2 + 160 - 28*m**3 - 260*m = 0.
-2, 2/5, 5
Let y = -2 - -17. Suppose 2*z - 10 = 0, 9 + y = 3*x + 3*z. Suppose 18*j**2 - 9 + 7*j**2 + 10*j + 9 - 35*j**x = 0. Calculate j.
-2/7, 0, 1
Suppose -29*z - 32 = -31*z - 4*j, -2*z + 14 = j. Let u(i) be the second derivative of 11*i + 0 - 2/3*i**3 + 0*i**2 - 1/6*i**z. Solve u(t) = 0.
-2, 0
Suppose 4*w - 5*d = 43, 3*d = 3*w + 4*d - 37. Factor -8*l**2 - 20*l**2 + w + 8*l**3 - 2*l + 0*l**2 + 10*l**2.
2*(l - 2)*(l - 1)*(4*l + 3)
Suppose 4*g - 4*o - 117 = 31, -g - 3*o = -49. Let d(j) be the first derivative of 40*j**3 - 2 - g*j**2 + 0*j + j**5 - 45/4*j**4. Factor d(w).
5*w*(w - 4)**2*(w - 1)
Let b be (-4 - -2) + -407 + -6 + -1. Let p be (b/40 + 10)/(-2). Let 38416/5 - 10976/5*u + 1176/5*u**2 - 56/5*u**3 + p*u**4 = 0. Calculate u.
14
Suppose -76*r = -100*r. Suppose -141*i + 49*i = r. Factor 28/9*l**3 + i + 32/9*l + 8*l**2.
4*l*(l + 2)*(7*l + 4)/9
Let q be ((-4)/(-12))/((-2)/(-246)). Let m = 43 - q. Solve -18 - 4 - 20*l - 2 - 4*l**m = 0.
-3, -2
Let a(q) be the first derivative of -q**6/900 + q**5/18 + q**4/180 - 5*q**3/9 - 15*q**2/2 + 2*q + 180. Let t(p) be the second derivative of a(p). Factor t(h).
-2*(h - 25)*(h - 1)*(h + 1)/15
Suppose 65*n = 59*n + 30. Factor -33*f**2 + 11*f**3 - 1021*f**4 + 50 + 510*f**4 + n*f + 510*f**4.
-(f - 5)**2*(f - 2)*(f + 1)
Let a(x) be the first derivative of -x**7/840 + 5*x**6/96 + x**5/240 - 25*x**4/96 - 69*x**2/2 - 247. Let v(k) be the second derivative of a(k). Factor v(r).
-r*(r - 25)*(r - 1)*(r + 1)/4
Let n(h) be the third derivative of h**5/300 - 37*h**4/40 + 54*h**3/5 + h**2 - 1256. Find a, given that n(a) = 0.
3, 108
Let x(b) be the third derivative of -3*b**4/4 - 43*b**3/3 + 68*b**2. Let k be x(-5). Factor -2/3*z**k - 2/15*z**5 + 8/15*z**2 - 4/5*z**3 + 0 + 16/15*z.
-2*z*(z - 1)*(z + 2)**3/15
Let f be 3/(6/(-40)*-2). Suppose f*c + 28 = 48. Solve -5/4*r**c - 3/4 + 7/4*r + 1/4*r**3 = 0 for r.
1, 3
Let x(l) be the first derivative of -l**6/6 + 4*l**5 - 32*l**4 + 256*l**3/3 - 2781. Factor x(n).
-n**2*(n - 8)**2*(n - 4)
Let v(p) be the third derivative of -3/4*p**5 - 35/24*p**4 - 5/3*p**3 + 0*p - 1/42*p**7 - 1 - 5/24*p**6 - 150*p**2. Find s such that v(s) = 0.
-2, -1
Let b = -121948 - -365878/3. Solve -b*v**3 + 8*v**5 - 4/9 + 10/3*v + 38/9*v**4 - 34/9*v**2 = 0.
-1, 2/9, 1/4, 1
Let r(p) be the third derivative of -3/56*p**4 + 0*p + 0*p**3 - 101*p**2 - 1/140*p**5 + 0. Factor r(w).
-3*w*(w + 3)/7
Let r(j) = 7*j**3 - 9*j**2 - j + 3. Let a(g) = 30*g**3 - 38*g**2 - 5*g + 13. Let t(m) = 6*a(m) - 26*r(m). Determine h, given that t(h) = 0.
0, 1, 2
Let h(l) be the third derivative of l**5/60 - 25*l**4/24 - 66*l**3 - 2377*l**2. Factor h(t).
(t - 36)*(t + 11)
Let o(x) be the second derivative of -x**4/8 + x**3/3 + 5*x**2 - 586*x. Factor o(t).
-(t + 2)*(3*t - 10)/2
Let v(f) = -f**2 + 31*f - 48. Let l be v(30). Let x be -6*3/l*(-6 - -9). Factor 0*k + 0 + 1/2*k**x + 0*k**2 - 1/4*k**4.
-k**3*(k - 2)/4
Let i(h) = 2*h**2 + 2*h + 3. Let a be i(-3). Suppose 0 = l - 6*l + a. Factor -7*p**5 + 5*p**5 - 5*p**4 - 10*p**3 - l*p**5 - 10*p**4.
-5*p**3*(p + 1)*(p + 2)
Let o = 40985/144 + -4529/16. Suppose -o*m - 4 + 2/9*m**2 = 0. What is m?
-2, 9
Let l be (184/12 - 1) + (9/5)/((-22)/110). Determine i so that 2/3*i**3 + l*i**2 - 8*i + 0 - 2/3*i**4 = 0.
-3, 0, 2
Suppose 291*p - 3*p**3 + 212*p + 153*p**2 - 52*p - 133*p = 0. Calculate p.
-2, 0, 53
Let a(t) = 2*t**2 - 114*t - 669. Let f(i) = 8*i**2 - 344*i - 2014. Let s(d) = -10*a(d) + 3*f(d). Let s(x) = 0. Calculate x.
-18, -9
Let r be (15/45*-3)/(10/(-6)). Factor -99/5 - r*i**2 + 102/5*i.
-3*(i - 33)*(i - 1)/5
Suppose -4*m - 4*v - v = 6, 2*m + 4*v + 6 = 0. Let c be (m + (-17)/18)/(73/292). Determine x, given that -20/9*x - 2/3 - 4/3*x**3 - c*x**4 - 8/3*x**2 = 0.
-3, -1
Determine y so that 2/17*y**4 + 90/17*y - 42/17*y**2 + 0 - 2/17*y**3 = 0.
-5, 0, 3
Factor -542/3*k + 2/3*k**3 - 268/3*k**2 - 272/3.
2*(k - 136)*(k + 1)**2/3
Suppose -4 - 6 = -2*l, 0 = 4*x + 3*l - 31. Suppose -5*v - 24 = h, 30 = h + x*h - 5*v. Suppose h - 1/2*p - 1/2*p**2 = 0. Calculate p.
-2, 1
Let r(o) be the first derivative of 55 - 5/3*o**3 + 200*o**2 - 8000*o. Factor r(n).
-5*(n - 40)**2
Suppose -8*v = -22 - 82. Factor 64 - 32*u**3 - 47*u**2 + 14*u - v*u**2 + 18*u - 4*u**4.
-4*(u - 1)*(u + 1)*(u + 4)**2
Determine f, given that 7458*f**2 + 1855*f - 13920*f**2 + 7502*f**2 + 400*f + 1801*f + 2*f**4 - 98*f**3 = 0.
-3, 0, 26
Let u(k) = 57 - 6*k - 4 + k. Let g be u(10). Find o such that 5/2*o + 0 + 5*o**4 - 5/2*o**g - 5*o**2 = 0.
-1, 0, 1/2, 1
Let -8190*p**2 + 3/2*p**3 + 14905800*p - 9042852000 = 0. Calculate p.
1820
Let k = 175 + -173. What is g in 0*g**5 + g**5 + 1250*g**2 - 5*g**3 + 2*g**4 - 1256*g**k = 0?
-3, -1, 0, 2
Let w(i) = -i**3 - 6*i**2 + 6*i - 1. Let y be w(-7). Let c be 3/(-3) - (-52 + 10). Factor y*k - 8*k + c + 5*k - 35 - 9*k**2.
-3*(k - 1)*(3*k + 2)
Let g = 419 + -417. Factor 28*x - 32 + 118 - 62 + 4*x**g.
4*(x + 1)*(x + 6)
Let y be 1525/95 + (-699 - -688). Let -y*b**2 - 162/19 - 252/19*b - 4/19*b**3 + 2/19*b**4 = 0. Calculate b.
-3, -1, 9
Let x(f) be the first derivative of -f**4/3 - 10*f**3/3 + 12*f**2 - 82*f + 32. Let g(r) be the first derivative of x(r). Factor g(y).
-4*(y - 1)*(y + 6)
Let g(b) = -2*b**2 + 2*b + 1. Let o(k) = -19*k**2 - 62*k + 83. Suppose -2 = r + j, 14*j = 3*r + 16*j + 6. Let q(m) = r*g(m) + o(m). Solve q(f) = 0 for f.
-27/5, 1
Suppose -31*f + 33*f + h = 15, -4*f = 4*h - 20. Suppose -f*u - 44 = -32*u. Find q, given that 15/2 + 6*q - 3/2*q**u = 0.
-1, 5
Let y(f) be the first derivative of 7*f**5/4 - 205*f**4/8 - 215*f**3/4 + 95*f**2 + 65*f + 5595. Let y(a) = 0. Calculate a.
-2, -2/7, 1, 13
Factor 326/7*f + 0 + 2/7*f**2.
2*f*(f + 163)/7
Let n(h) = -9*h**3 + 1763*h**2 - h - 4. Let a(j) = -4*j**3 - 2*j**2 - j - 4. Let u(v) = -a(v) + n(v). Factor u(i).
-5*i**2*(i - 353)
Let s(j) = -8*j**3 + 897*j**2 - 2*j - 892. Let t(v) = -3*v**3 + 448*v**2 - v - 446. Let o(y) = -2*s(y) + 5*t(y). Factor o(w).
(w - 1)*(w + 1)*(w + 446)
Suppose -2*x = -56*z + 60*z + 14, -5*x = 4*z + 53. Let -4/7 + 6/7*l + 116/7*l**z + 64/7*l**2 + 22/7*l**5 + 12*l**4 = 0. Calculate l.
-1, 2/11
Determine d so that -338/3*d**2 + 316/3*d - 646/3*d**3 - 16 + 56/3*d**4 = 0.
-1, 1/4, 2/7, 12
Let c = -57 - -121. Suppose -15*x + c = x. Factor -61*k**2 + 120*k**2 - 62*k**2 - x*k**3 + 7*k - 2 + 2*k.
-(k - 1)*(k + 2)*(4*k - 1)
Let -162024*z**2 + 4060*z - 76728*z**2 + 8 + 10266*z**2 - 12 + 4252077*z**3 - 20 + 1442897*z**4 = 0. What is z?
-3, 2/113
Suppose k - 6*k = 0. Suppose -w = -k*w - 36. Factor 2*a**3 - w*a + 4*a**2 + 38*a + 0*a**3.
2*a*(a + 1)**2
Let c(x) be the second derivative of -1/30*x**5 - 2*x**2 - 1/6*x**4 - 16*x + 1/60*x**6 + 0 + 0*x**3. Let y(d) be the first derivative of c(d). Factor y(k).
2*k*(k - 2)*(k + 1)
Let l = 54 - 215/4. Let g = 49097 - 49095. Determine x so that -1/4 + l*x - 1/4*x**3 + 1/4*x**g = 0.
-1, 1
Let j(u) be the second derivative of -u**5/100 + u**4/60 + 13*u**3/15 + 12*u**2/5 - 283*u. Factor j(x).
-(x - 6)*(x + 1)*(x + 4)/5
Let p(b) be the second derivative of -b**4/3 + 374*b**3/3 + 376*b**2 + 10*b - 16. Fact