et p(y) be the first derivative of -3/2*y**2 - 4/3*y**3 + 1/6*y**6 + 4/5*y**5 + 0*y + 1/2*y**4 - 31. Determine i, given that p(i) = 0.
-3, -1, 0, 1
Let b(c) be the second derivative of 26*c + 0*c**2 + 5/2*c**3 + 1 + 1/12*c**4. Factor b(r).
r*(r + 15)
Let p = -37 + 39. Let v(c) = -11*c**2 - 27*c - 10. Let q(r) = -2*r**2. Let a(s) = p*v(s) - 6*q(s). Let a(x) = 0. Calculate x.
-5, -2/5
Let k = -361360 - -361362. Factor 21/2 - 27/4*c + 3/4*c**k.
3*(c - 7)*(c - 2)/4
Suppose -2*f + 11 = z, 5*f + 4*z - 32 = f. Determine y, given that -15*y**3 - 13*y**3 - 3*y - 2*y**2 - 4*y - 4 + 29*y**f = 0.
-1, 4
Let r(f) = -f**3 + 8*f**2 - 6*f - 5. Let o be r(7). Determine b, given that -6*b**2 + 4*b**2 + 15*b + b**2 - 12 - 2*b**o = 0.
1, 4
Let r(m) be the third derivative of 13*m**7/840 - 7*m**6/60 + m**5/10 - m**4/24 - 41*m**3/6 + m**2 - 14. Let i(b) be the second derivative of r(b). Factor i(h).
3*(h - 2)*(13*h - 2)
Let z = -316 - -318. Find n such that 415*n - 219*n - 221*n + 5*n**z = 0.
0, 5
Let o(w) be the first derivative of -2*w**5/5 - 37*w**4/2 + 26*w**3 + 37*w**2 - 76*w - 577. Suppose o(t) = 0. Calculate t.
-38, -1, 1
Let n(t) = 114*t - 8. Let u be n(-2). Let w = 240 + u. Determine p, given that -3*p**2 - 51/5*p**3 + 12*p**w + 0 + 6/5*p = 0.
-2/5, 0, 1/4, 1
Let n(a) be the first derivative of 2*a**3/27 - 1274*a**2/9 + 811538*a/9 + 3902. What is r in n(r) = 0?
637
Let g(l) = 3*l + 35. Let r be g(-11). Factor -18*y + 1081*y**2 - 5*y - y - 1085*y**r.
-4*y*(y + 6)
Let u = 7 - -5. Let p be (20/u)/((-1)/(-12)*4). What is m in m**2 - 3*m**4 + 6*m**4 - 11*m**5 + 9*m**3 + 2*m**p - 4*m**2 = 0?
-1, 0, 1/3, 1
Let h = 30999/2 - 15499. Determine l so that -1/6*l**2 + h*l - 1/3 = 0.
1, 2
Let u be 44 - 630/(150/10). Find i, given that -20/3*i + 56/3*i**u - 3*i**4 + 0 - 11*i**3 = 0.
-5, 0, 2/3
Factor -212/3*x - 4/3*x**2 - 320.
-4*(x + 5)*(x + 48)/3
Let u be (8 - -4 - -6)*(-10)/15. Let x be (-18)/21*-7 + (6 - u). Solve -x + 4*j + 16/3*j**2 - 4/3*j**3 = 0.
-2, 3
Let m(g) be the first derivative of g**6/2340 + g**5/12 + 16*g**4/39 - 14*g**3/3 + 7*g + 100. Let s(t) be the third derivative of m(t). Factor s(p).
2*(p + 1)*(p + 64)/13
Let c(x) be the second derivative of -x**6/30 + x**5/4 + x**4/4 - 13*x**3/6 - 5*x**2 - x + 76. Factor c(r).
-(r - 5)*(r - 2)*(r + 1)**2
Let z(c) = -c**2 + 4*c + 142. Let a be z(14). Suppose -5*n - 2*m + 8 = 4, 2*n + m - a = 0. Determine d, given that n + 3/5*d**2 + 0*d + 1/5*d**3 = 0.
-3, 0
Let p = 311326/105 - 2965. Let d(i) be the third derivative of -18*i**2 + 4/21*i**3 + 0 + 0*i - p*i**5 + 1/42*i**4. Suppose d(r) = 0. Calculate r.
-1, 2
Suppose 0 = -l - 8*l + 27. Factor -w + 28*w**l - 12*w**4 + 21*w**3 - 48*w**3 + 12*w**2.
-w*(w - 1)*(w + 1)*(12*w - 1)
Let i(a) be the first derivative of 0*a - 15/2*a**4 - 15*a**3 + 5*a**5 + 5*a**2 - 21. Factor i(o).
5*o*(o - 2)*(o + 1)*(5*o - 1)
Let z(u) be the first derivative of -25*u**3/3 + 40*u**2 + 45*u + 2. Let r = -50 - -51. Let l(b) = b**2 - b. Let f(o) = r*z(o) + 30*l(o). Factor f(a).
5*(a + 1)*(a + 9)
Let u = 174556/122199 + 2/17457. Let n be ((-7)/(-49))/(1/2). Suppose -8/7 - n*o**2 + u*o = 0. Calculate o.
1, 4
Let a be 1260/(-90) - (-674)/48. Let g(o) be the third derivative of a*o**4 + 0 - 1/12*o**5 + 36*o**2 - 1/120*o**6 + 0*o + 5/6*o**3. Factor g(w).
-(w - 1)*(w + 1)*(w + 5)
Let p = -3 + 3. Let y = -19610209/7 - -2801459. Let -1/7*u**3 + y*u - 1/7*u**4 + p + 4/7*u**2 = 0. Calculate u.
-2, -1, 0, 2
Suppose 2*n + d + 11 = 4*d, -8 = 2*n - 2*d. Let p be (7 - (-184)/(-24))/n. Suppose -p*a**3 + 2*a**2 - 2*a + 2/3 = 0. What is a?
1
Let x(d) be the first derivative of 2*d**5/65 - 31*d**4/26 - 278*d**3/39 - 41*d**2/13 + 420*d/13 + 2461. Find o, given that x(o) = 0.
-3, -2, 1, 35
Suppose -490 = 118*y - 128*y. Let v be (y + -22)*(-2)/(-18). Factor v*w**3 + 9/2*w**2 + 0 - 3/2*w**4 + 0*w.
-3*w**2*(w - 3)*(w + 1)/2
Let a(f) = -f**3 + 5*f**2 + f - 3. Let l be a(5). Determine u, given that -32*u**3 - l*u + 48*u**3 - 14*u**3 = 0.
-1, 0, 1
Let h(m) = -m**3 - 2*m**2 - 16*m - 93. Let c be h(-4). Let k(o) be the second derivative of -2/3*o**c + 8*o**2 + 0 - 4/3*o**4 - 21*o + 1/5*o**5. Factor k(v).
4*(v - 4)*(v - 1)*(v + 1)
Let d(h) be the first derivative of -h**5/6 + 7*h**4/6 + 7*h**3/3 - 5*h**2/3 - 97*h - 32. Let s(o) be the first derivative of d(o). Factor s(u).
-2*(u - 5)*(u + 1)*(5*u - 1)/3
Factor 9772*g - 4*g**3 - 1507*g**2 - 27312 + 22424 - 3373*g**2.
-4*(g - 1)**2*(g + 1222)
Factor -2/9*h**2 + 58/3 + 52/9*h.
-2*(h - 29)*(h + 3)/9
Let p(q) be the first derivative of -q**3/15 + 1123*q**2/5 - 1261129*q/5 + 9316. Determine x so that p(x) = 0.
1123
Let t = -28 - 44. Let p = t - -74. Determine a so that -2*a + a**3 - 1 + 7*a**p + 4*a + 3*a**3 = 0.
-1, 1/4
Let v(g) be the first derivative of g**4/38 - 124*g**3/57 + 1281*g**2/19 - 17640*g/19 - 566. Let v(t) = 0. Calculate t.
20, 21
Suppose 501 - 7 = -19*u. Let b be u/(-21) - 20/210. Factor -10/7*y**2 + b*y**3 - 2/7*y**4 + 4/7*y + 0.
-2*y*(y - 2)*(y - 1)**2/7
Let c(n) be the third derivative of 5*n**8/21 + 26*n**7/35 + 3*n**6/5 - n**5/15 + 793*n**2. Factor c(f).
4*f**2*(f + 1)**2*(20*f - 1)
Determine x so that 2*x**5 + 298*x**2 + 19*x**3 - 6*x**4 - 274*x**2 - 2*x**5 - x**5 = 0.
-8, -1, 0, 3
Let j(h) be the third derivative of -h**8/24 - 23*h**7/105 + 11*h**6/30 + 46*h**5/15 + 2*h**4 + 55*h**2 + 46. What is i in j(i) = 0?
-3, -2, -2/7, 0, 2
Suppose 1704*y = 137 - 137. Suppose 5/2*k**2 + 165/2*k + y = 0. What is k?
-33, 0
Let z(o) be the second derivative of -o**4/42 - 68*o**3/21 - 132*o**2/7 + o - 669. Suppose z(y) = 0. Calculate y.
-66, -2
Let t(p) = 2*p**2 - 52*p + 53. Let g be t(25). Solve -25*a**g - 97086 + 10*a**2 - 5*a**5 + 97086 + 20*a**4 = 0.
0, 1, 2
Let w be (-4 - (-2 - (10 - 4)))*1. Let p = w + -2. Factor -32*a - 49*a**p + 128 - 52*a**2 + 103*a**2.
2*(a - 8)**2
Suppose 4*c = -3*w - 50, -3*w - 64*c + 90 = -70*c. Factor -4/9*u**3 - 20/9*u**w - 4/3 - 28/9*u.
-4*(u + 1)**2*(u + 3)/9
Let b be (352/15)/(13824/5760). Factor b*p - 20/9*p**2 - 4/9*p**3 - 64/9.
-4*(p - 2)*(p - 1)*(p + 8)/9
Let k = -390124/65 - -6002. Let n(g) be the first derivative of -k*g**5 - 11/26*g**4 - 9/13*g**2 - 4/13*g - 10/13*g**3 + 6. Let n(r) = 0. Calculate r.
-1, -2/3
Let p(h) be the third derivative of -h**7/1260 - 11*h**6/720 + 7*h**5/180 + h**4/6 + h**2 + 109*h - 2. Solve p(q) = 0.
-12, -1, 0, 2
Let c(g) = 2*g**2 + 11*g - 2. Let j be c(-6). Factor 20*i**3 + 246 - 2*i**2 - 246 - 3*i**2 - 20*i + 5*i**j.
5*i*(i - 1)*(i + 1)*(i + 4)
Let o(y) = 4*y**3 - 2*y**2 - 13*y + 3. Let j be o(4). Factor 284*u**3 + 125*u**4 + 216*u + 365*u**2 - 78*u**3 + j*u**2 + 244*u**3.
u*(5*u + 6)**3
Let c = -3211/2 + 481651/300. Let b(t) be the third derivative of 0*t - 1/15*t**3 - 1/40*t**4 - 19*t**2 - c*t**5 + 0. Factor b(k).
-(k + 1)*(k + 2)/5
Let s = -741509 - -6673583/9. Solve -34/9*m + s*m**2 + 32/9 = 0.
1, 16
Let i be (-60990)/(-150) - (-1)/(-10). Let m = 408 - i. Find o such that 0*o + 0 - 81/2*o**2 + 81/2*o**3 - 27/2*o**4 + m*o**5 = 0.
0, 3
Let x(v) = 10*v**2 + 524*v - 316. Let z be x(-53). Solve -24389/2 - 87/2*y**z - 2523/2*y - 1/2*y**3 = 0 for y.
-29
Let j(h) be the second derivative of -3/2*h**2 - 9/4*h**4 - 2 - 36*h - 5/2*h**3 - 1/5*h**6 - 21/20*h**5. Find u, given that j(u) = 0.
-1, -1/2
Suppose -4*t + 7*t - 14 = 5*l, 2*t - l - 14 = 0. Suppose 5*u - 7*p + t*p - 12 = 0, -2*u - 5*p = 9. Factor -2/3*h**2 - 2 - 2/3*h**u + 10/3*h.
-2*(h - 1)**2*(h + 3)/3
Let o(w) = -3*w**2 - 33*w - 8. Let r be o(-8). Find d such that -r*d**2 + 110*d**2 + 35*d - 61*d**2 - 15 + 5 = 0.
1/3, 2
Suppose -1696*k = -1707*k - 110. Let p be 4*k*30/(-400). Let -2/3 - 4*f**p + 4*f + 2/3*f**2 = 0. What is f?
-1, 1/6, 1
Suppose -216 = -3*x - 3*d, x - 3*d = -0*d + 84. Suppose -a = -x + 75. Factor 0*s**2 - 6/5*s**3 + a + 0*s - 3/5*s**5 + 9/5*s**4.
-3*s**3*(s - 2)*(s - 1)/5
Let p = 61/3001 + 2879/6002. Find w, given that p*w**2 - 5/6*w**3 + 0 + 1/3*w = 0.
-2/5, 0, 1
Let a(u) be the first derivative of -21*u**6/10 + 78*u**5/5 + 739*u**4/10 + 336*u**3/5 + 241*u**2/10 + 18*u/5 - 1608. Suppose a(r) = 0. What is r?
-2, -1/3, -1/7, 9
Factor -1/3*j**5 + 101/3*j**4 - 1174/3*j**2 - 1381/3*j - 165 - 62*j**3.
-(j - 99)*(j - 5)*(j + 1)**3/3
Determine r, given that 191/2*r**4 + 566*r**3 + 328 - 1468*r + 2*r**5 + 953/2*r**2 = 0.
-41, -4, 1/4, 1
Le