
-343, 0
Let x = 704/27 - -70/27. Let o = x - 28. Factor o*h + 0 + 1/3*h**2.
h*(h + 2)/3
Let p(g) be the third derivative of g**5/140 + 17*g**4/7 + 655*g**3/14 + 17*g**2 - 46*g - 2. Determine f so that p(f) = 0.
-131, -5
Find g such that 72*g**3 - 4*g**4 - 296*g**2 - 227*g - 493*g - 400 + 52*g**2 = 0.
-1, 10
Let n = -197 - -200. Let 5*l**n - l**3 - 4*l + 14 - 26 + 12*l**2 = 0. Calculate l.
-3, -1, 1
Let x(s) = -7*s**3 - 10*s**2 - 5*s - 2. Let o(u) = 8*u**3 + 10*u**2 + 5*u + 3. Let v = -42 - -45. Suppose -v*b - 3 = 3. Let r(d) = b*o(d) - 3*x(d). Factor r(h).
5*h*(h + 1)**2
Let n be (63 - 58) + 3/((-3)/4). Let f be (n + 0)*7*8/196. Factor -2/7*l**4 + f*l**3 + 2/7*l**2 - 2/7*l + 0.
-2*l*(l - 1)**2*(l + 1)/7
Suppose 669 = -12*m + 969. Suppose -38*c + 19*c = -m*c. Factor c + 2/3*a**2 + 2*a.
2*a*(a + 3)/3
Let l(t) = t**2 - t + 46. Let f be l(0). Suppose -47*u = -f*u - 2. Factor 36*w**u - 14/3*w**3 - 64/3 - 64*w.
-2*(w - 4)**2*(7*w + 2)/3
Let h(s) = s**3 + 5*s**2 - 3*s + 6. Let p be h(-4). Factor -1638 - p*j**2 + 1683 - 45*j + 14*j**2.
-5*(j + 3)*(4*j - 3)
Let p = -864271/28 - -30867. Let v(o) be the second derivative of 3/14*o**2 + 0 + p*o**4 + 3/7*o**3 - 16*o. Factor v(s).
3*(s + 1)*(5*s + 1)/7
Suppose -234 + 79*u**2 + 1/2*u**3 + 309/2*u = 0. Calculate u.
-156, -3, 1
Let u(o) be the second derivative of -37/30*o**3 - 1/60*o**4 - 113*o + 0*o**2 + 0. Determine r, given that u(r) = 0.
-37, 0
Let z(g) be the second derivative of 54*g - 1/6*g**3 + 0*g**2 - 1/20*g**5 + 0 + 1/6*g**4. Determine b, given that z(b) = 0.
0, 1
Suppose -3*f + 6*f = 84. Solve 20*t**2 - 64 + f*t**2 - 16*t - 49*t**2 = 0 for t.
-8
Suppose -245 - 1/4*y**2 + 249/4*y = 0. What is y?
4, 245
Suppose -149*k + 154*k + 8 = 4*j, 4*k - 2 = -j. Let 0 + 15/2*r**4 - 9/2*r + 33/2*r**j - 39/2*r**3 = 0. What is r?
0, 3/5, 1
Let y = -548 - -45491/83. Let h = y - -75/1079. Factor 54/13*f**2 - 50/13*f**3 - 22/13*f + 16/13*f**4 + h.
2*(f - 1)**3*(8*f - 1)/13
Let -1940/9*a - 2/9*a**2 - 470450/9 = 0. What is a?
-485
Suppose 4*m - 68 - 12 = 0. Let s be (-14)/(-5) - m/25. Factor -45*q**2 - 2*q + 3 + 19*q**2 + 27*q**s - 2.
(q - 1)**2
Suppose 56*m**2 - 10*m + 50*m - 8*m**2 - 15*m**2 - 29*m**2 + 84 = 0. Calculate m.
-7, -3
Let v = -1864 + 1786. Let y be (48/5)/12*(-15)/v. Factor 6/13 + 8/13*q + y*q**2.
2*(q + 1)*(q + 3)/13
Let j(b) be the second derivative of 2*b**4/3 + 90*b**3 - 136*b**2 + 441*b - 2. Factor j(u).
4*(u + 68)*(2*u - 1)
Factor -91/2*w + 17/2*w**2 - 1/2*w**3 + 147/2.
-(w - 7)**2*(w - 3)/2
Suppose -5474*j = 1786*j. Factor -45*b**2 + 0*b + 5/4*b**4 + j + 175/4*b**3.
5*b**2*(b - 1)*(b + 36)/4
Let x = -107 + 372. Factor -3*y**3 + 6*y**4 + y - 534*y**5 - 6*y**2 - y + x*y**5 + 272*y**5.
3*y**2*(y - 1)*(y + 1)*(y + 2)
Suppose -27*y + 1332 = -801. Solve 126*a + 199 - y - 296*a + 5*a**3 + 45*a**2 = 0.
-12, 1, 2
Let z(g) = -g**3 - 14*g**2 - 4*g + 13. Let r be z(-11). Let t be (r/15)/6 + 4. Let -24/5*w**3 + 72/5*w**2 + t*w**4 + 48/5 - 96/5*w = 0. Calculate w.
2
Let d(k) be the third derivative of k**6/360 + 7*k**5/180 - k**4/12 - 4*k**3 - 3349*k**2. Factor d(a).
(a - 3)*(a + 4)*(a + 6)/3
Let x(h) be the third derivative of h**7/168 - h**6/9 - 16*h**3 + 77*h**2. Let y(w) be the first derivative of x(w). Solve y(p) = 0 for p.
0, 8
Factor 1215/4 + 3/4*t**3 - 987/4*t - 231/4*t**2.
3*(t - 81)*(t - 1)*(t + 5)/4
Let o = 340193/5 + -68038. Let -o*a**3 - 33/5*a**2 + 0 - 6*a = 0. Calculate a.
-10, -1, 0
Let j(p) be the first derivative of -p**3/21 + 433*p**2/7 - 865*p/7 + 2660. Suppose j(s) = 0. What is s?
1, 865
Let v = -7133 + 7133. Let i(u) be the third derivative of 0*u**5 + 0 - 1/660*u**6 + v*u**3 + 0*u**4 + 17*u**2 + 0*u. Factor i(b).
-2*b**3/11
Let b(p) = 15541*p + 528397. Let l be b(-34). Factor -2/21*v**l - 2/7*v - 10/21*v**2 + 6/7.
-2*(v - 1)*(v + 3)**2/21
Factor -17/8*m**3 + 5/4 + 77/8*m - 35/4*m**2.
-(m - 1)*(m + 5)*(17*m + 2)/8
Let i(z) = z**2 - 11*z + 29. Let f be i(13). Factor -1514*n**2 + f*n**2 - 9 + 216*n + n**2 + 1.
-2*(27*n - 2)**2
Let l(u) be the third derivative of -11/28*u**4 + 43*u**2 + 0*u + 1/21*u**5 + 12/7*u**3 - 1/420*u**6 + 0. Let l(g) = 0. Calculate g.
3, 4
Let z(q) = -q**3 - q**2 + 12*q. Let d(i) = -135*i**2 - 23*i + 66*i**2 + 2*i**3 + 71*i**2. Let l(x) = -6*d(x) - 11*z(x). Factor l(s).
-s*(s - 2)*(s + 3)
Factor 243/5 + 27*k + 9/5*k**2 - 3/5*k**3.
-3*(k - 9)*(k + 3)**2/5
Let g(k) be the second derivative of 5*k**4/18 + 7*k**3/9 + 7137*k. Factor g(h).
2*h*(5*h + 7)/3
Let t(i) = -43*i**2 + 1489*i + 12. Let k(m) = 144*m**2 - 4468*m - 40. Let j(o) = 3*k(o) + 10*t(o). Find u such that j(u) = 0.
-743, 0
Let g(d) be the third derivative of -1/90*d**6 - d**2 + 0 + 4/45*d**5 + 82*d - 2/315*d**7 + 0*d**3 + 2/9*d**4. Factor g(v).
-4*v*(v - 2)*(v + 1)*(v + 2)/3
Suppose -41 + 13 = 4*u. Let r be (-19)/u + 7/((-98)/(-4)). Let -4/7 - 2/7*i + 4/7*i**2 + 2/7*i**r = 0. Calculate i.
-2, -1, 1
Let z be (-16)/56 + (5 - 16880/(-35)). Let k = 983/2 - z. Suppose 0*v**3 - k + 3/2*v**4 - 9*v**2 + 12*v = 0. What is v?
-3, 1
Let v be 104/65*-5*1/(-2). Factor 81*j**2 - 3*j**5 - 57*j**3 - 332*j - 9*j**v + 192*j**3 - 536*j + 2916 - 949*j - 127*j.
-3*(j - 3)**3*(j + 6)**2
Let c(x) be the first derivative of -19*x**3/12 + 5*x**2/2 - 5296. Factor c(u).
-u*(19*u - 20)/4
Let o(v) be the first derivative of -27*v**2 + 0*v - 11*v**3 + 3 - 3/4*v**4. Factor o(c).
-3*c*(c + 2)*(c + 9)
Let y = -575091 - -1725278/3. Factor 10/3 + s**2 - y*s**3 - 1/3*s**4 + 17/3*s.
-(s - 2)*(s + 1)**2*(s + 5)/3
Let g = 61 - 51. Suppose -t + 6*t - g = 0. Determine y so that -y - 168*y**t + 168*y**2 + y**3 = 0.
-1, 0, 1
Let -1/2*s**4 - 15 + 19/2*s**2 + 11/2*s + 1/2*s**3 = 0. What is s?
-3, -2, 1, 5
Let p(y) = -146*y - 2041. Let h be p(-14). Let c(k) be the second derivative of -40*k + 1/5*k**2 + 0 + 1/100*k**5 + 1/6*k**h + 1/15*k**4. Solve c(v) = 0.
-2, -1
Let o(s) be the third derivative of -s**6/60 + 13*s**5/15 + 29*s**4/3 + 40*s**3 - 9*s**2 - 15. Let o(p) = 0. What is p?
-2, 30
Let y(n) be the second derivative of -n**7/14 + 64*n**6/5 - 3072*n**5/5 + n + 258. Factor y(r).
-3*r**3*(r - 64)**2
Let m(o) = -o + 8. Let l be m(3). Factor -11 - 16*s + 0 - l*s**2 - 2*s**3 + 3 - 5*s**2.
-2*(s + 1)*(s + 2)**2
Let a(j) be the first derivative of -7*j**4/26 + 12154*j**3/39 - 1319360*j**2/13 + 376712*j/13 + 1814. Determine f so that a(f) = 0.
1/7, 434
Let f(v) = v**3 + 19*v**2 + 4*v + 10. Let i be f(-19). Let o = 70 + i. Factor -8*s**3 + 4*s + 89 - 12*s - 12*s**2 - 91 - 2*s**o.
-2*(s + 1)**4
Let z(l) be the first derivative of 2*l**5/5 - 63*l**4/2 + 682*l**3 - 961*l**2 + 426. Suppose z(k) = 0. Calculate k.
0, 1, 31
Let l(k) be the third derivative of -k**5/105 - 10*k**4/21 - 38*k**3/21 + 6*k**2 + 23*k. Solve l(p) = 0.
-19, -1
What is g in -12/7*g - 24/7 - 3/7*g**5 + 30/7*g**2 + 15/7*g**3 - 6/7*g**4 = 0?
-2, -1, 1, 2
Let 0*h - 122/7*h**4 - 512/7*h**3 + 2/7*h**5 + 0 - 520/7*h**2 = 0. Calculate h.
-2, 0, 65
Let m(l) = 3*l**2 - 978*l - 1282. Let u(d) = 8*d**2 - 3108*d - 3847. Let n(c) = 7*m(c) - 2*u(c). Factor n(q).
5*(q - 128)*(q + 2)
Let v(z) be the third derivative of z**8/1512 + 8*z**7/189 + 113*z**6/540 + 37*z**5/135 + 1257*z**2. Solve v(f) = 0.
-37, -2, -1, 0
Let y(l) be the third derivative of -l**8/840 + l**7/35 - 6*l**6/25 + 56*l**5/75 - 11085*l**2. Factor y(x).
-2*x**2*(x - 7)*(x - 4)**2/5
Determine m, given that -1/2*m**4 + 4333/2*m**2 + 6066 + 162*m**3 + 8070*m = 0.
-6, -1, 337
Let m be ((-1664)/8736)/((-1)/(6/4)). Suppose 4*n + p = 11, n = -0*p - 5*p + 17. Factor 8/7 - m*y**3 + 12/7*y**n - 18/7*y.
-2*(y - 4)*(y - 1)**2/7
Let h(k) = -206*k**2 + 3450*k - 15130. Let o(p) = 138*p**2 - 2302*p + 10087. Let m(q) = -5*h(q) - 7*o(q). Factor m(b).
(8*b - 71)**2
Let y = -20064 + 20070. Factor 9/2*w - y - 3/4*w**2.
-3*(w - 4)*(w - 2)/4
Let f = -1856 - -1858. Suppose -3*i + 225 = -0*i. Factor 375*b**5 - 24*b + 390 - 390 - i*b**4 + 124*b**2 + 32*b**f - 270*b**3.
3*b*(b + 1)*(5*b - 2)**3
Let v = 410/2667 + 23/1778. Factor v*s + 0 - 1/3*s**2 + 1/6*s**3.
s*(s - 1)**2/6
Let r(l) be the third derivative of 7/30*l**3 + 0*l + 1/20*l**4 - 1/300*l**5 + 0 + 45*l**2. Determine p, given that r(p) = 0.
-1, 7
Let s be (-14)/(-24) + (-10)/30. Let t(f) be the second derivative of -3*f**2 + 14*f - 1/2*f**3 + s*f**4 + 0. Let t(i) = 0. Calculate i.
-1, 2
Suppose 203*g + 7604 