 the second derivative of p**5/20 - 5*p**4/6 - 17*p**3/6 + 33*p**2 - 818*p. Suppose y(r) = 0. What is r?
-3, 2, 11
Let z(j) be the first derivative of 147*j**4/4 + 483*j**3 - 900*j**2 + 528*j - 7276. Suppose z(r) = 0. What is r?
-11, 4/7
Let g(k) = k**2 - 12*k - 317. Let x be g(26). Let -105*a**2 + 20*a**3 - x*a**2 - 60*a**2 + 26 + 112*a + 27 + 27 = 0. Calculate a.
-2/5, 1, 10
Let i = 4/6295 + 6279/25180. Factor -i*w**2 - 81 + 9*w.
-(w - 18)**2/4
Let g(d) = -d**3 + 26*d**2 - 26*d + 39. Let i be g(25). Suppose 2*s**2 - 2904 + 2810 + 78*s + i*s = 0. Calculate s.
-47, 1
Let a(b) be the third derivative of -b**7/140 - 59*b**6/240 + 13*b**5/12 + 1351*b**4/12 + 294*b**3 + 7*b**2 + 410. Determine y, given that a(y) = 0.
-14, -2/3, 9
Let k = 2595/4529 + -1/647. Let i(m) = m**3 + m**2 - 4*m + 2. Let o be i(1). Factor 0*h - k*h**3 - 2/7*h**2 + o - 2/7*h**4.
-2*h**2*(h + 1)**2/7
Find d, given that 78732/7 + 3/7*d**4 + 32076/7*d + 198/7*d**3 + 4239/7*d**2 = 0.
-27, -6
Let k = 1099 - 1099. Let y(n) be the third derivative of -1/540*n**6 + 0*n**4 + 5*n**2 + k*n**3 + 0 + 0*n - 1/270*n**5. Determine q, given that y(q) = 0.
-1, 0
Suppose 13 = 15*g - 27 - 35. Let a(w) be the second derivative of -7/90*w**6 + 0*w**2 - 11*w + 0 + 1/12*w**g + 2/9*w**3 + 4/9*w**4. Factor a(j).
-j*(j - 2)*(j + 1)*(7*j + 2)/3
Let o = 448 - 316. Factor -14*l**3 - 44*l + 24 - o*l**2 - 25*l**3 + 17*l**3 - 14*l**3 + 28*l**4.
4*(l - 3)*(l + 1)**2*(7*l - 2)
Let n(g) be the third derivative of -g**7/42 + 11*g**6/24 - 13*g**5/4 + 245*g**4/24 - 50*g**3/3 + 2554*g**2. Factor n(k).
-5*(k - 5)*(k - 4)*(k - 1)**2
Let y = 162 + -152. Factor 6*m**3 - 28*m**2 + y*m**2 + 2*m + 3*m**4 + 15*m**2 - 8*m.
3*m*(m - 1)*(m + 1)*(m + 2)
Let w(k) be the first derivative of -2*k**3/3 - 107*k**2 - 624*k + 5400. Factor w(d).
-2*(d + 3)*(d + 104)
Let q(n) be the second derivative of 4*n**6/35 - 5*n**5/7 + 4*n**4/3 - 8*n**3/21 - n + 1122. Find u such that q(u) = 0.
0, 1/6, 2
Let o(s) be the second derivative of -s**5/16 + 45*s**4/16 - 125*s**3/12 + 2980*s. Let o(k) = 0. What is k?
0, 2, 25
Let r = -104029/9 + 11559. Find y such that -r*y**2 + 4/9 - 2/9*y = 0.
-2, 1
Let l = 3/194 + 47/97. Let j(z) be the second derivative of 3/20*z**5 + 0 + 1/10*z**6 - 1/4*z**4 + 0*z**2 - l*z**3 + 18*z. Let j(a) = 0. Calculate a.
-1, 0, 1
Suppose 2*h - 69 = -2*p + 11, 5*h - 220 = 5*p. Let z be 153/h - 6/12. Suppose -10/7*x**3 + z*x - 12/7 + 24/7*x**2 = 0. Calculate x.
-1, 2/5, 3
Let l(y) be the first derivative of -y**4/12 + 124*y**3/9 + 2241. Factor l(m).
-m**2*(m - 124)/3
Let m be 816/(-14) + 8/28. Let b = -48 - m. Factor b*f**4 + 10*f**2 + 24*f**3 + 5*f + 11*f**3 + 10*f**2 - 10*f**3.
5*f*(f + 1)**2*(2*f + 1)
Let n = -60424 - -60429. Let 2/11*d**n + 16/11*d**2 - 4/11*d**4 + 0*d + 0 - 8/11*d**3 = 0. What is d?
-2, 0, 2
Let t(h) be the third derivative of -h**5/570 - 2*h**4/57 + 35*h**3/19 - 64*h**2 + 2. Solve t(x) = 0 for x.
-15, 7
Let v be 365*1*(-1230)/(-13325) - 12. Let 70/13*u + v*u**3 - 6/13 - 18*u**2 - 112/13*u**4 = 0. Calculate u.
1/7, 3/8, 1
Factor -8464 + 552*d - 12*d**2 + 2/23*d**3.
2*(d - 46)**3/23
Let w(b) = 4*b**2 + 401*b - 385. Let o(y) = 2*y**2 + 200*y - 194. Let f(m) = 5*o(m) - 2*w(m). Let f(g) = 0. What is g?
-100, 1
Factor -3/5*k**3 + 0*k**2 + 9/5*k + 6/5.
-3*(k - 2)*(k + 1)**2/5
Let f(j) be the first derivative of j**4 + 232*j**3/3 - 2*j**2 - 232*j + 3842. Factor f(n).
4*(n - 1)*(n + 1)*(n + 58)
Let y(o) be the second derivative of o**4/12 - o**3 + 3*o**2/2 - 18*o. Let f be y(6). Factor 128*n + 48 + 85*n**2 + 28*n**f - 104*n**2 - 113*n**2.
4*(n - 3)*(n - 2)*(7*n + 2)
Let l(i) be the second derivative of i**4/18 - 527*i**3/9 - 1058*i**2/3 - 664*i - 2. Suppose l(y) = 0. What is y?
-2, 529
Let l = -4231 - -4235. Let d(h) be the first derivative of 8/9*h**2 - 5 - 1/18*h**l - 8/3*h + 2/27*h**3. Suppose d(c) = 0. What is c?
-3, 2
Let v be 2/16*26 + (-5)/20. Suppose 5*a + 2 + 43 = 2*q, q - 20 = 3*a. Factor 9 + q*b + v*b**2 - 11*b + 39.
3*(b + 4)**2
Suppose 4*v = 4*b + 12, -2*v + 3*b - 2*b = -8. Suppose -2 = -v*f + 2*c + 2, f + 5*c = -10. Factor f*n + 2*n - 3*n - 5*n + 3*n**2 + 3.
3*(n - 1)**2
Let u = 18011 + -18007. Factor -75/2 - 1/6*d**u + 10*d + 13/3*d**2 - 2/3*d**3.
-(d - 3)**2*(d + 5)**2/6
Find r, given that -67*r - 135/2 + 1/2*r**2 = 0.
-1, 135
Let a = 1172638 - 1172635. Factor -132/7 - 4/7*n**a - 20*n**2 - 268/7*n.
-4*(n + 1)**2*(n + 33)/7
Determine w so that 216*w**3 + 1796*w**2 - 622*w**3 - 624*w**3 + 864 - 845*w**3 + 154*w**2 + 3168*w = 0.
-12/25, 2
Let h(w) be the first derivative of 2/35*w**5 + 28*w**3 + 2*w**4 - 43 + 686*w + 196*w**2. Factor h(y).
2*(y + 7)**4/7
Let h(d) be the second derivative of 8/7*d**4 + 1/49*d**7 - 32/7*d**3 + 4 - 1/7*d**6 + 48/7*d**2 + 15*d + 6/35*d**5. Factor h(y).
6*(y - 2)**3*(y - 1)*(y + 2)/7
Let y = 162296/275961 + 2/16233. Factor y*w - 12/17 - 2/17*w**2.
-2*(w - 3)*(w - 2)/17
Let 388*s**2 + 5411*s - 5419*s + 435*s**4 + 300*s**4 + 1666*s**3 = 0. Calculate s.
-2, -2/7, 0, 2/105
Let u be (5 + -2 + 0)*7/7. Let 174946*a**2 - 174946*a**2 + u*a**3 - 27*a**4 = 0. Calculate a.
0, 1/9
Let i = 48074 + -48070. Factor -9/2*l + 1/2 + i*l**2.
(l - 1)*(8*l - 1)/2
Solve 7290*o**4 - 75*o**3 + 20*o**5 - 25*o**2 + 75*o - 7290*o**4 + 45 = 0 for o.
-1, 3/2
Let 126/5 + 13*p + 1/5*p**2 = 0. What is p?
-63, -2
Solve 9*x**4 + 248*x + 32*x**3 - 12 - 204*x**2 - 2*x**4 + 26*x**3 + 108 - 88*x**2 = 0 for x.
-12, -2/7, 2
Factor -4705*o + 16135*o - 618*o - 16723837 + 6982225 - 3*o**2.
-3*(o - 1802)**2
Suppose -37*r + 41*r - 184 = 0. Determine u so that -2*u**3 + 73*u**2 + 3*u - 23 - r*u**2 - 4 - u**3 = 0.
-1, 1, 9
Let n(i) = 5*i - 53. Let p be n(11). Let c(l) be the first derivative of -1/3*l**p - 4*l - 14 + 2/9*l**3. Suppose c(y) = 0. Calculate y.
-2, 3
Let z = 770671/1284435 - 2/256887. Factor -42/5*k - z*k**3 - 21/5*k**2 - 24/5.
-3*(k + 1)*(k + 2)*(k + 4)/5
Let r(p) = 3*p**3 - 82*p**2 - 241*p + 288. Let b(s) = -s**3 + 12*s**2 - 3. Let u(o) = -20*b(o) - 5*r(o). Find h such that u(h) = 0.
-23, -12, 1
Let v(y) be the second derivative of 7*y**5/60 - 649*y**4/36 - 422*y**3/9 - 94*y**2/3 + 10048*y + 1. Factor v(j).
(j - 94)*(j + 1)*(7*j + 2)/3
Let o(j) = -j**2 + 8*j - 43. Let l be o(6). Let n = l - -36. Factor 11*p**4 + 4*p**4 - 7 + 20*p**5 + 7 - n*p**3.
5*p**3*(p + 1)*(4*p - 1)
Let s(y) be the first derivative of -9/2*y + 55 - 24*y**2 - 128/3*y**3. Factor s(w).
-(16*w + 3)**2/2
Factor -2/7*n**3 + 118/7*n**2 + 0 + 780/7*n.
-2*n*(n - 65)*(n + 6)/7
Suppose 3*f = -g + 8, -1 + 9 = 4*g. Solve -2/3*r**3 + 8/3 - 8*r + 2/3*r**5 + 22/3*r**2 - f*r**4 = 0.
-2, 1, 2
Let c(b) be the first derivative of 40*b + 5/3*b**3 - 15*b**2 - 15. Factor c(p).
5*(p - 4)*(p - 2)
Suppose 0 = 36*y - 23 - 49. Let 5*t**y + 3*t**3 + 1467*t + 12*t**3 + 60 - 1567*t = 0. What is t?
-3, 2/3, 2
Find w, given that 2/3*w - 2/3*w**3 + 1988/3 - 1988/3*w**2 = 0.
-994, -1, 1
Let u = -58/401 + 2489/14436. Let n(s) be the third derivative of 0 - 1/135*s**5 + 0*s + 0*s**4 + 0*s**3 - u*s**6 + 26*s**2. Factor n(i).
-2*i**2*(15*i + 2)/9
Find k such that 12 - 83/7*k - 1/7*k**2 = 0.
-84, 1
Let t(p) be the first derivative of 6*p**2 + 0*p - 1/40*p**5 - 21 + 0*p**4 + p**3. Let w(g) be the second derivative of t(g). Suppose w(y) = 0. Calculate y.
-2, 2
Let l(a) be the first derivative of a**4/8 - 4*a**3 + 1024*a + 721. Suppose l(h) = 0. What is h?
-8, 16
Suppose 2*m = -2*y + 1414, -857 + 150 = -m - 5*y. Let p = m + -6355/9. Factor 8/9 + 2/9*w**2 + p*w.
2*(w + 2)**2/9
Let j(t) be the third derivative of -t**7/210 + 53*t**6/30 - 2809*t**5/15 + 5*t**2 + 562*t. Find m, given that j(m) = 0.
0, 106
Let w(d) be the first derivative of 1/15*d**5 + 3*d + 91 + 22/9*d**3 + 2/3*d**4 + 4*d**2. Factor w(l).
(l + 1)**2*(l + 3)**2/3
Factor -3*n**3 - 1/3*n**4 - 24 + 28*n - 2/3*n**2.
-(n - 2)*(n - 1)*(n + 6)**2/3
Let x(w) = -40*w**5 + 82*w**4 + 312*w**3 - 740*w**2 + 388*w - 20. Let b(r) = -2*r**3 - 2*r**2 - 4*r - 1. Let h(n) = -4*b(n) + 2*x(n). Solve h(v) = 0 for v.
-3, 1/20, 1, 3
Let n(c) be the first derivative of c**5/10 - c**4 + 3*c**3 - 4*c**2 - 83*c + 1. Let i(v) be the first derivative of n(v). Factor i(x).
2*(x - 4)*(x - 1)**2
Let r(q) = -64*q**3 + 2*q**2 + 3*q + 2. Suppose 6 = -5*g + 1. Let y be r(g). Factor -20 - 31*x**2 - 20*x - 25*x**3 + y*x**2 + 31*x**2.
-5*(x - 2)*