 = 74*k**2 - 243*k + 1101. Let s(n) = -7*i(n) + 4*l(n). Factor s(o).
2*(o - 54)*(o - 5)
Suppose -2*g = l, 0*g + 10 = g + 3*l. Let c be g/(-8) + 22/8. Factor 0*k**2 + 2*k**4 - k + k**2 + k**3 + 0*k**2 - c*k**4.
-k*(k - 1)**2*(k + 1)
Let y be (41459/(-616) - -69) + (8/(-14))/1. Let u be (-57)/(-108) + 2/9. Factor 0 + 0*d - 3/8*d**4 + y*d**2 + u*d**3.
-3*d**2*(d - 3)*(d + 1)/8
Let j = 104914/157317 - 12/52439. Determine r so that -j*r**2 - 20 + 26/3*r = 0.
3, 10
Let y(n) be the third derivative of -n**5/30 + 64*n**3/3 + 53*n**2 - 2*n + 18. Find i, given that y(i) = 0.
-8, 8
Suppose -3*s = -5*s + 40. Let w = s - 12. Let j(k) = 12*k**3 - 8*k**2 - 12*k. Let q(r) = 8*r**3 - 5*r**2 - 8*r. Let v(b) = w*q(b) - 5*j(b). Solve v(x) = 0.
-1, 0, 1
Let w(x) be the second derivative of 0 - 1/210*x**5 + 1/420*x**6 + 5*x - 1/7*x**3 - 5/2*x**2 - 5/84*x**4. Let y(o) be the first derivative of w(o). Factor y(h).
2*(h - 3)*(h + 1)**2/7
Let a be (-16)/(-21)*(-4554)/(-4048). Factor -2/7*f**4 - 4/7*f**2 + 0 + a*f**3 + 0*f.
-2*f**2*(f - 2)*(f - 1)/7
Let f(p) be the third derivative of p**6/300 - 51*p**5/50 + 494*p**4/5 - 5776*p**3/15 + 2638*p**2. Suppose f(q) = 0. Calculate q.
1, 76
Let g(x) be the first derivative of -35/8*x**2 - 109 + 5/4*x**3 - 15/2*x. Factor g(j).
5*(j - 3)*(3*j + 2)/4
Let h = -157617 + 1103325/7. Find i such that -19/7*i**2 - 3/7*i + 0 - 29/7*i**4 - 39/7*i**3 - h*i**5 = 0.
-3, -1, -1/2, -1/3, 0
Let m(y) be the third derivative of y**6/600 - 7*y**5/300 + 7*y**4/60 - 4*y**3/15 + 219*y**2. Solve m(r) = 0 for r.
1, 2, 4
Let s be (11 - 484/44)/(0 - -3). Solve 5*u**4 + 0*u**3 + 5/2*u - 5*u**2 - 5/2*u**5 + s = 0 for u.
-1, 0, 1
Let g be (3 + -44)/1*1. Let x = 45 + g. Determine h so that h**5 + 7*h - 12*h**x - 7*h - 15*h**3 - 4*h**5 - 6*h**2 = 0.
-2, -1, 0
Suppose -10*r + 14*r + 4 - 4 = f, -4*r = -4*f. Factor -2/11*w**4 + 0 + f*w + 2/11*w**2 + 0*w**3.
-2*w**2*(w - 1)*(w + 1)/11
Let a(b) be the second derivative of b**5/4 + 10*b**4 + 200*b**3/3 + 1532*b. Determine c so that a(c) = 0.
-20, -4, 0
Let j(q) = q + 3. Let p be j(-1). Factor -7*a**p + 14 + 3*a**3 - 6 - 4.
(a - 2)*(a - 1)*(3*a + 2)
Let s(g) be the first derivative of 32/9*g**3 - 3*g + 140 - 2*g**2. Factor s(b).
(4*b - 3)*(8*b + 3)/3
Let s(n) = -7*n + 245. Let x be s(35). Suppose -2*a = 3 - 9. Let 0*i**2 - 2 - 3*i - 5*i**2 + 2*i**a + 8*i**2 + x*i = 0. What is i?
-2, -1/2, 1
Let s(l) be the third derivative of l**6/540 - 2*l**5/27 - 121*l**4/108 - 100*l**3/27 - 2609*l**2. Find k, given that s(k) = 0.
-4, -1, 25
Let k(h) be the third derivative of -h**7/21 - 1367*h**6/80 - 42473*h**5/24 - 4556*h**4 - 867*h**3 + 6979*h**2. Let k(j) = 0. Calculate j.
-102, -1, -1/20
Factor y**5 + 171*y**2 + 190*y**2 - 5*y + 15*y**3 - 355*y**2 - 11*y**3 - 6*y**4.
y*(y - 5)*(y - 1)**2*(y + 1)
Suppose -250/3*d + 44/3*d**2 + 2/3*d**3 - 364 = 0. What is d?
-26, -3, 7
Let j(b) be the second derivative of -11*b**5/40 + 13*b**4/12 - 19*b**3/12 + b**2 - 3929*b. Factor j(v).
-(v - 1)**2*(11*v - 4)/2
Suppose 0 = 13*a + 2063 + 1603. Let b = -1127/4 - a. Factor -3/4*g**2 + 1/4*g**4 + 1/2 - b*g + 1/4*g**3.
(g - 1)**2*(g + 1)*(g + 2)/4
Let g(a) be the third derivative of -a**6/24 - 169*a**5/2 - 3375*a**4/8 - 2530*a**3/3 + 1450*a**2. Factor g(y).
-5*(y + 1)**2*(y + 1012)
Suppose 27*x + 23/4*x**3 - 1/4*x**4 + 26*x**2 + 0 = 0. What is x?
-2, 0, 27
Let m = 1504958/205197 + -60/68399. Factor -m*n - 1/3 - 7*n**2.
-(n + 1)*(21*n + 1)/3
Find n, given that -3/7*n**2 - 816/7 - 414/7*n = 0.
-136, -2
Let r be ((-3114)/(-6055))/((-4)/(-5)). Let q(l) be the second derivative of 7*l + 1/70*l**6 + 3/20*l**5 + r*l**4 + 10/7*l**3 + 12/7*l**2 + 0. Solve q(g) = 0.
-2, -1
Suppose -60*h + 14*h = -138. Let -37*i**3 - 12*i + 33*i**4 + 10*i**h - 51*i**2 + 19*i**2 - 40*i**2 = 0. What is i?
-1, -2/11, 0, 2
Determine v, given that -410 - 306 + 297*v + 379 - 71 - 3*v**2 - 732 = 0.
4, 95
Let d be (-6 + -4)/((3800/(-60))/19). Let 122/5*m + 16/5 + 4*m**4 + 193/5*m**d + 279/5*m**2 = 0. Calculate m.
-8, -1, -2/5, -1/4
Let w(i) = 6*i**3 + 80*i**2 - 411*i + 673. Let j(f) = f**3 + 16*f**2 - 82*f + 134. Let x(v) = -22*j(v) + 4*w(v). Factor x(r).
2*(r - 8)*(r - 4)**2
Let n(u) be the second derivative of -u**7/23940 - u**6/380 - 27*u**5/380 + 31*u**4/12 - 2*u - 28. Let v(o) be the third derivative of n(o). Factor v(j).
-2*(j + 9)**2/19
Let x(n) be the first derivative of -2*n**6/15 + 11*n**5/25 + 23*n**4/4 + 28*n**3/15 - 1790. Determine w, given that x(w) = 0.
-4, -1/4, 0, 7
Let a(d) be the third derivative of -3*d**2 + 0 - 5/24*d**3 - 9*d + 1/48*d**5 + 0*d**4. Solve a(c) = 0 for c.
-1, 1
Suppose 286 = -23*d - 59. Let q be (-7)/((-154)/12)*(-5)/d. Find j such that 2/11*j**3 - 4/11*j**2 + 0 + q*j**4 + 0*j = 0.
-2, 0, 1
Let z = 1/74268 - -1930961/519876. Determine a so that -z*a - 2/7*a**2 - 24/7 = 0.
-12, -1
Let i be 15/12 - (-532)/304. Let a(r) be the third derivative of 0 + 1/210*r**5 + 0*r**i - 1/28*r**4 - 4*r**2 + 0*r. Find z such that a(z) = 0.
0, 3
Let x(h) = -20*h**3 + 104*h**2 + 162*h + 50. Let k(b) = -41*b**3 + 209*b**2 + 325*b + 97. Let g(j) = -2*k(j) + 5*x(j). Determine t so that g(t) = 0.
-2/3, 7
Let 7*p**5 - 39*p**4 - 186*p**3 - 51 - 85*p - 116*p - 294*p**2 - 4*p**5 = 0. What is p?
-1, 17
Let n(m) be the first derivative of 228*m**5/25 - 463*m**4/10 + 736*m**3/15 - 13*m**2/5 - 12*m/5 - 3732. What is t in n(t) = 0?
-2/19, 1/6, 1, 3
Suppose 125126 - 124802 = 162*y. Let -3*k**4 + y*k + 1/3*k**5 + 7*k**3 - 19/3*k**2 + 0 = 0. What is k?
0, 1, 6
Suppose -2*h = -3*j - 4, -3*j - j + 10 = 5*h. Suppose 2106 - 2110 = -d. Factor 0 + 1/4*o**2 + 1/2*o**3 + j*o + 1/4*o**d.
o**2*(o + 1)**2/4
Suppose -41*w + 24*w + 306 = 0. Determine o, given that 17*o - 20*o**2 - 6*o + 11*o - 10*o**3 + 5*o**4 + w*o = 0.
-2, 0, 2
Let r(b) = 2*b**3 + 4*b**2 - b + 1. Let v(t) = -2*t**4 - 6*t**3 + 24*t**2 + 52*t + 4. Let p(a) = -4*r(a) + v(a). Suppose p(z) = 0. What is z?
-7, -2, 0, 2
Let g(j) be the first derivative of j**8/420 - 8*j**3 + 50. Let i(w) be the third derivative of g(w). Determine b so that i(b) = 0.
0
Factor 119*z - 3*z**2 + 97*z + 469 + 12*z + 0*z + 242.
-3*(z - 79)*(z + 3)
Solve -1350/7*j**2 + 72/7*j**3 + 200*j - 1/7*j**4 + 2625 = 0 for j.
-3, 5, 35
Let x(n) be the first derivative of 87 + 6/5*n**3 + 1/20*n**4 + 17/10*n**2 + 0*n. Let x(m) = 0. Calculate m.
-17, -1, 0
Let b be (-1332)/12654*646/(-10). Factor b*q - 12 - 2/5*q**2.
-2*(q - 15)*(q - 2)/5
Let p be 10550/(-80)*(-6)/1580. Let g = p - 1/1264. Let 1/2*r - 1/2*r**2 + 1/2 - g*r**3 = 0. What is r?
-1, 1
Let -52271*f**4 + 15*f**5 + 105*f**3 - 13*f**2 + 52351*f**4 + 13*f**2 = 0. What is f?
-3, -7/3, 0
Let n**5 - 40/3*n**3 - 32 + 80/3*n**2 - 14/3*n**4 + 112/3*n = 0. Calculate n.
-2, 2/3, 2, 6
Let d(y) = -2*y**3 - 107*y**2 - 1673*y - 1575. Let n(l) = l**2 + l - 1. Let h(i) = -d(i) + 7*n(i). Factor h(q).
2*(q + 1)*(q + 28)**2
Suppose -616 = 11*k - 304 - 312. Let t(n) be the second derivative of 0 + 1/6*n**3 + k*n**2 - 1/48*n**4 + 16*n. Solve t(h) = 0.
0, 4
Let i be (10 + -4)*(-1 - -2) + -4. Factor -a**2 - a**i + 13*a**2 - 2 - a**2 + 19*a.
(a + 2)*(10*a - 1)
Let p = -4058214/7 + 584529. Determine m so that -p*m + 680943/7 - 3/7*m**3 + 549/7*m**2 = 0.
61
Let o(a) be the second derivative of a**5/20 + 53*a**4/12 + 60*a**3 + 2*a - 8228. Determine l, given that o(l) = 0.
-45, -8, 0
Suppose 4*f - 734 = -2*k, -2*k + 381 + 349 = 3*f. Let j = 361 - k. Factor 4 + 10/3*c**j + 34/3*c.
2*(c + 3)*(5*c + 2)/3
Let u(a) be the first derivative of 4*a**5/5 - 6*a**4 - 124*a**3/3 + 312*a**2 + 720*a + 633. Let u(s) = 0. What is s?
-5, -1, 6
Let i(f) = 18*f - 284. Let p be i(16). Suppose 0 = -p*z - z + 4*t + 20, 3*z - 20 = 4*t. Factor 8/9*r**2 + 2/3*r + z + 2/9*r**3.
2*r*(r + 1)*(r + 3)/9
Suppose -8*g + 3*g = -5. Let z be 1*g/(4/(-12)) - -5. Factor 40*n**2 + 8*n + 55*n**2 - 28*n**3 - 115*n**z.
-4*n*(n + 1)*(7*n - 2)
Let f = -210930 - -210933. Let -2/3*y**2 - 5/3*y + y**f + 4/3 = 0. Calculate y.
-4/3, 1
Suppose 4*z - 306 = -54. Let l = z - 30. Suppose -4*d**2 - l*d + d + 31 - 3 + 8 = 0. What is d?
-9, 1
Let j(y) be the third derivative of y**6/30 - 11*y**5/3 + 364*y**4/3 + 1568*y**3/3 - 520*y**2. What is f in j(f) = 0?
-1, 28
Suppose 55*w - 3*o = 60*w + 21, -4*w - 5*o = 9. Let m be -3 - (-295)/50 - w/(-15). Let 5/4 + 0*r**2 - 5/4*r**4 - m*r**3 + 5/2*