Let j(l) = -7*l**4 + 25*l**3 + 1372*l**2 + 7266*l + 2690. Let a(c) = -22*c**4 + 76*c**3 + 4117*c**2 + 21799*c + 8071. Let g(t) = 2*a(t) - 7*j(t). Factor g(x).
(x - 21)*(x + 8)**2*(5*x + 2)
Let z(q) be the third derivative of q**5/90 - 947*q**4/18 + 896809*q**3/9 - 391*q**2. Factor z(i).
2*(i - 947)**2/3
Suppose 0 = 34*l + 96 - 96. Let y(j) be the second derivative of -1/30*j**6 + 0*j**2 + 1/12*j**4 - 1/20*j**5 - 8*j + 1/6*j**3 + l. Let y(h) = 0. What is h?
-1, 0, 1
Let -9/5*h**2 + 9/5*h**4 + 1/5*h**5 - 1/5*h**3 + 0 + 0*h = 0. What is h?
-9, -1, 0, 1
Let x = -2334 + 20566/9. Let q = x - -2227/45. Factor q*s**2 - 12/5 - 3/5*s**3 + 12/5*s.
-3*(s - 2)*(s - 1)*(s + 2)/5
Let i(o) be the second derivative of 1/45*o**5 - 1/189*o**7 - 2*o + 2/135*o**6 + 7/27*o**3 - 2/9*o**2 + 39 - 4/27*o**4. Factor i(t).
-2*(t - 1)**4*(t + 2)/9
Suppose -d + 22 + 8 = 0. Let t = -2392 - -2394. Let 4 - 20*m**t - 5*m - 4 + m**3 - 6*m**3 + d = 0. Calculate m.
-3, -2, 1
Suppose 0 = -2*x + w - 2 + 7, 5*x - 8 = -2*w. Let b be 1/(16/40 - 6/40). Let -320*n**3 - 5*n**4 + n**b + 308*n**3 - 8*n**x = 0. Calculate n.
-2, -1, 0
Let y = 36 + -34. Let n(h) = -11*h. Let g be n(-2). Suppose -12 + 35*f**y - 185*f + g + 10 + 105*f = 0. Calculate f.
2/7, 2
Factor 140*p - 23584 + 23584 + 116*p**2 - 23*p**3 + p**4.
p*(p - 14)*(p - 10)*(p + 1)
Let l(r) be the third derivative of -1/300*r**5 - 57*r**2 - 10/3*r**3 + 0*r - 1/6*r**4 + 0. Solve l(w) = 0.
-10
Let m be ((-39)/24 - -2) + (-25041)/408 + 61. Determine u, given that 6/11*u**2 + 2/11*u**3 + 4/11*u + m = 0.
-2, -1, 0
Let d(x) = 13*x**2 + 2171*x - 2164. Let t(g) = -12*g**2 - 2169*g + 2163. Let p(b) = -9*d(b) - 10*t(b). Find a such that p(a) = 0.
-718, 1
Let b(x) = -10*x**3 + 87*x**2 + 37*x + 13. Let i(f) = -2*f**3 + 22*f**2 + 9*f + 3. Suppose -29*g = 2*g - 806. Let k(a) = g*i(a) - 6*b(a). Factor k(j).
2*j*(j + 6)*(4*j + 1)
Let p(k) be the first derivative of 1/420*k**5 - 25 - 1/7*k**4 + 0*k + 24/7*k**3 + 2*k**2. Let d(w) be the second derivative of p(w). Let d(l) = 0. What is l?
12
Let q(v) be the first derivative of 56*v**3/15 - 10*v**2 - 156*v/5 + 1521. Solve q(t) = 0 for t.
-1, 39/14
Suppose -24*m + 6 = -20*m + 3*l, 0 = -5*m - 4*l + 7. Let k(r) be the second derivative of 2/27*r**m + 11*r - 1/54*r**4 + 0 + 0*r**2. Factor k(x).
-2*x*(x - 2)/9
Suppose -299*n - 357*n + 110*n + 1932 = 98*n. Factor -40/9*b + 16/9*b**n + 4/3 - 4*b**2.
4*(b - 3)*(b + 1)*(4*b - 1)/9
Let a(m) be the third derivative of 26*m**7/105 + 8*m**6/3 - 79*m**5/15 - 7*m**4/3 + 16122*m**2. Let a(x) = 0. Calculate x.
-7, -2/13, 0, 1
Let m(a) be the first derivative of a**3/12 + 17*a**2/4 + 33*a/4 - 1611. Solve m(f) = 0.
-33, -1
Factor 70/3 - 1/6*p**2 - 139/6*p.
-(p - 1)*(p + 140)/6
Let p(v) = 36*v**2 + 57*v - 1485. Let u(t) = 61*t**2 + 113*t - 2970. Let h(m) = 5*p(m) - 3*u(m). Determine n, given that h(n) = 0.
-33, 15
Let c(f) be the first derivative of 3*f**4/8 - 22*f**3 + 480*f**2 - 4608*f + 1271. Find z, given that c(z) = 0.
12, 16
Let f(q) = -9*q**3 - 432*q**2 + 13. Let u(g) = -7*g**3 - 324*g**2 + 10. Let d(t) = -10*f(t) + 13*u(t). Factor d(i).
-i**2*(i - 108)
Factor -1/2*h**4 + 253/2*h**2 + 116*h + 10*h**3 + 0.
-h*(h - 29)*(h + 1)*(h + 8)/2
Let h = -426626 + 426630. Factor 8/3*d**h + 0*d + 2/3*d**5 + 0*d**2 + 2*d**3 + 0.
2*d**3*(d + 1)*(d + 3)/3
Let x = 25475/3 + -50803/6. Factor -1/2*u**3 + 0 - x*u + 7*u**2.
-u*(u - 7)**2/2
Let z = 280432/9 + -31152. Let k(n) be the first derivative of 288*n + 326*n**3 + z*n**6 - 736/15*n**5 - 9 - 10/3*n**4 + 504*n**2. What is i in k(i) = 0?
-3/4, 4
Let w(z) be the first derivative of z**6/10 + 3*z**5/20 - 3*z**4/4 - 5*z**3/2 - 3*z**2 + 69*z + 75. Let v(b) be the first derivative of w(b). Factor v(d).
3*(d - 2)*(d + 1)**3
Let i be (1/2)/(57/570). Suppose -36 = -7*n - i*n. Find t, given that 4/3*t**4 + 0 + 2/3*t - 2/3*t**n - 4/3*t**2 = 0.
-1, 0, 1/2, 1
Let u(a) be the second derivative of 0*a**2 - a - 4/3*a**3 - 7/9*a**4 - 1/15*a**5 + 227. Let u(o) = 0. Calculate o.
-6, -1, 0
Let j(l) be the first derivative of -l**4/2 + 46*l**3/3 + 136*l**2 + 224*l - 1791. Suppose j(t) = 0. Calculate t.
-4, -1, 28
Factor -1149*o + 1077*o - 7*o**2 + o**3 + 5*o**2 - 76 - 13*o**2.
(o - 19)*(o + 2)**2
Let 10533*b**2 + 24 - 5*b**4 + 564*b**5 - 10510*b**2 + 9*b**3 - 50*b - 563*b**5 - 2*b**4 = 0. What is b?
-2, 1, 3, 4
Let -100/3*b**2 + 0 + 2/3*b**3 + 98/3*b = 0. Calculate b.
0, 1, 49
Let c(u) = 31*u + 26*u - 56*u - 1. Let p(g) = -g**2 + 34*g - 357. Let i(n) = 4*c(n) + p(n). Suppose i(s) = 0. Calculate s.
19
Suppose -3*p - 545 = -4*k, -k + 4*p = -124 - 22. Let q = k + -134. Determine l so that 2/5*l**4 + 0 - 1/5*l**3 - 1/5*l**5 + 0*l**2 + q*l = 0.
0, 1
Let u(a) be the first derivative of 8/13*a + 2/39*a**3 - 4/13*a**2 + 101. Factor u(x).
2*(x - 2)**2/13
Let a be ((-234)/(-702))/(20/3). Let w(t) be the first derivative of -1/4*t - 1/2*t**2 - 1/4*t**4 - 8 - a*t**5 - 1/2*t**3. Let w(p) = 0. What is p?
-1
Let i(x) be the third derivative of -x**6/540 + 103*x**5/90 - 2002*x**4/9 + 23716*x**3/27 - 290*x**2 - 2. Factor i(h).
-2*(h - 154)**2*(h - 1)/9
Let q(k) = 2*k + 16. Let p be q(-7). Factor 9*j - 2*j - j + 3*j**3 + 12*j**p + 3*j.
3*j*(j + 1)*(j + 3)
Suppose 12*a = 7*a - 5, a - 1231 = 2*q. Let s = -613 - q. Factor 0 - 1/6*i**s - 1/6*i + 1/3*i**2.
-i*(i - 1)**2/6
Solve -119848/3*u - 364652/9*u**2 - 1706/9*u**3 - 2/9*u**4 + 80656 = 0.
-426, -2, 1
Let h(s) = 2*s**3 - 109*s**2 - 569*s + 667. Let j(c) = c**3 - 27*c**2 - 142*c + 166. Let v(o) = -2*h(o) + 9*j(o). Determine t, given that v(t) = 0.
-4, 1, 8
Factor -468/5*g + 912/5 + 6/5*g**2.
6*(g - 76)*(g - 2)/5
Let w(n) be the third derivative of n**8/1680 - 4*n**7/175 + 8*n**6/75 - 3*n**5/50 - 13*n**4/24 + 7*n**3/5 + 320*n**2 + 9. Suppose w(v) = 0. What is v?
-1, 1, 2, 21
Suppose 2/5*x**3 - 2022/5*x - 4036/5 + 2016/5*x**2 = 0. What is x?
-1009, -1, 2
Factor -45322*f**2 + 47430*f**2 - 722*f + 122*f - 28*f**3.
-4*f*(f - 75)*(7*f - 2)
Factor -94 - 356*a**4 + 72*a**5 - 130*a**3 + 346*a**4 - 67*a**5 - 235*a + 24 - 280*a**2.
5*(a - 7)*(a + 1)**3*(a + 2)
Let f(h) be the second derivative of 2*h**7/7 - 14*h**6/5 + 87*h**5/20 + 13*h**4 + 15*h**3/2 + 15*h - 12. Let f(o) = 0. What is o?
-1/2, 0, 3, 5
Let v(w) be the second derivative of -4*w**5 + 1430*w**4/3 - 44285*w**3/6 + 91035*w**2/2 + w - 3876. Suppose v(o) = 0. What is o?
17/4, 63
Let j(w) be the second derivative of -w**7/23940 + w**6/855 - w**5/95 - 15*w**4 - w - 28. Let c(p) be the third derivative of j(p). Factor c(s).
-2*(s - 6)*(s - 2)/19
Let 74*c**3 - 73*c**3 - 192*c**2 + 18 - 67*c + 64*c - 64*c**3 = 0. Calculate c.
-3, -1/3, 2/7
Let l(o) = -4*o + 51. Let g be l(7). Suppose 0 = 12*n + 23 - g. Factor -2/19*q**2 + 2/19*q + n.
-2*q*(q - 1)/19
Let p(o) be the third derivative of 2*o**2 - 1/42*o**7 + 1/3*o**4 - 7/120*o**6 + 1/60*o**5 - 1/336*o**8 + 0 - 11*o + 2/3*o**3. Determine c, given that p(c) = 0.
-2, -1, 1
Let w be (11 - (-849)/(-63))*(-11 + -2 + 296/32). Let x be ((-2 - 136) + 2)/(-7). Factor w*u + 16/7*u**3 + 8/7 + x*u**2.
(u + 8)*(4*u + 1)**2/7
Let p = 90716354/971961 + 2/323987. Factor 9800/3 + p*t + 2/3*t**2.
2*(t + 70)**2/3
Let g(b) be the first derivative of -b**4/2 - 8*b**3 + 15*b**2 + 52*b + 180. Factor g(y).
-2*(y - 2)*(y + 1)*(y + 13)
Let p(b) = b**2 + 7*b - 23. Let c be p(-8). Let q be ((-48)/c)/(1/5). Factor 14*t**2 - 13*t**2 + 21 - q*t + 43.
(t - 8)**2
Let c = -273 - 415. Let b = c + 1280. Factor -b + 5*x**5 + 5*x + 592 - 10*x**3.
5*x*(x - 1)**2*(x + 1)**2
Let z(g) = 2*g**3 - 6*g**2 + 2*g + 8. Let r be z(4). Let k = r - 45. Solve 7*a + k*a**2 - 4*a + 3 + 3*a = 0.
-1
Let 5928*a + 6267*a**2 - 1488*a**4 + 472 + 2433*a**3 + 3*a**5 + 1665*a**4 + 1448 = 0. What is a?
-40, -16, -1
Let v(g) be the second derivative of -g**6/720 + g**5/180 + g**4/48 - 58*g**2 + 165*g. Let a(w) be the first derivative of v(w). Suppose a(u) = 0. What is u?
-1, 0, 3
Let k be (1 + (-2 - 1))/2. Let z(c) = c - 1. Suppose -s + 10 = 7. Let t(i) = i**3 + i**2 + i - 3. Let y(w) = k*t(w) + s*z(w). Solve y(b) = 0 for b.
-2, 0, 1
Suppose -4*w + 483 + 453 = 0. Suppose -w + 34 = -4*b. Factor 9*p**3 - b*p**2 + 7*p**4 + 53*p**2 - 19*p**4.
-3*p**2*(p - 1)*(4*p + 1)
Suppose 2*p + 2044 = -2*x, 4*p = -37*x + 42*x - 4124. Let s = 2055/2 + p. Find g such that 9/2*g + 6 - s*g**2 = 0.
-1, 4
Let b be