
Let j(d) be the first derivative of d**7/3780 - d**6/1620 - d**5/270 - 2*d**3/3 + 2*d - 72. Let u(l) be the third derivative of j(l). Let u(m) = 0. Calculate m.
-1, 0, 2
Let z(q) = 23025*q + 23027. Let n be z(-1). Solve -64/11*r**n + 70/11*r - 18/11 - 8/11*r**3 = 0 for r.
-9, 1/2
Let q be 47 - (-92)/((-4876)/2385). Solve -27/2*s**5 - 819/8*s**4 - 177/4*s**3 + 681/8*s**q + 21/2 + 129/2*s = 0 for s.
-7, -2/3, -1/4, 1
Suppose 4*n = 42*f - 41*f + 3, -9*n - 2*f = 6. Let m = -1 - -1. Determine h, given that n*h + m - 1/8*h**2 = 0.
0
Let s(t) be the second derivative of 78*t + 10/9*t**3 + 1/2*t**5 - 1 - 23/12*t**4 + 7/90*t**6 + 2*t**2. Factor s(q).
(q - 1)**2*(q + 6)*(7*q + 2)/3
Let s be (9/(-6))/(-2 - (-9)/6). Suppose 82*k + 10*p = 5*p + 353, 0 = -5*k + 5*p - 5. Factor 4/5*i**4 + 32/5*i**2 - 16/5*i - k*i**s + 0.
4*i*(i - 2)**2*(i - 1)/5
Let y be (11/(-330)*-18)/((-64)/80) - 766/(-40). Suppose 0 + 2/5*d**2 - y*d = 0. Calculate d.
0, 46
Let w(a) be the first derivative of 0*a**2 + 4 + 2/5*a**3 + 1/30*a**4 - 10*a. Let t(k) be the first derivative of w(k). Factor t(d).
2*d*(d + 6)/5
Let n(u) be the first derivative of 3*u**4/22 - 4*u**3 - 303*u**2/11 - 468*u/11 + 1405. Factor n(g).
6*(g - 26)*(g + 1)*(g + 3)/11
Let h(a) = 107*a**2 - 24*a - 8. Let d(x) = 215*x**2 - 48*x - 14. Let o(f) = -4*d(f) + 7*h(f). Determine s, given that o(s) = 0.
0, 8/37
Let r be (0 + (-3)/(-1))/(-1) - -3. Suppose r = 5*j + 2*j - 329. Solve -73*n - 3*n**2 + j*n + 62*n - 108 = 0.
6
Find k such that -385371*k + 4*k**4 + 196309 - 2104*k**3 + 280852*k**2 + 1291297 - 397670 - 712917*k = 0.
2, 261
Suppose -12*i + 57 = 7*i. Factor 18 + 12 - i*k**2 + 15 - 42.
-3*(k - 1)*(k + 1)
Let c(o) be the first derivative of -250 + 7/18*o**3 - o - 19/12*o**2. Factor c(z).
(z - 3)*(7*z + 2)/6
Solve 235/2*j**2 + 478 - 1/2*j**3 + 476*j = 0 for j.
-2, 239
Let j = -95440 - -95440. Factor -2/7*n**2 - n**3 - 3/7*n**4 + j*n + 0.
-n**2*(n + 2)*(3*n + 1)/7
Let y(x) be the second derivative of 53*x - 29/21*x**3 + x**2 + 2/21*x**4 + 0. Determine i so that y(i) = 0.
1/4, 7
Let m(a) be the first derivative of a**5/10 + 11*a**4/6 + 10*a**3/3 - 8*a + 84. Let p(z) be the first derivative of m(z). Factor p(k).
2*k*(k + 1)*(k + 10)
Let r(j) = -11*j**3 - 27*j**2 - 57*j - 71. Let c(s) = -34*s**3 - 80*s**2 - 172*s - 221. Let d(h) = 6*c(h) - 19*r(h). Factor d(v).
(v + 1)**2*(5*v + 23)
Let z(y) be the third derivative of 0*y - 61*y**2 + 0 + 11/24*y**4 - 2*y**3 - 1/120*y**6 + 1/30*y**5. Let z(s) = 0. What is s?
-3, 1, 4
Let n be 0/(-7) + 1*-2*-1. Suppose -4*j + n*v = 3*v - 10, 10 = -5*v. Find r such that -2*r**4 + 205 - 205 - 4*r + 2*r**2 + r**3 + 3*r**j = 0.
-1, 0, 1, 2
Let f be 16/(-6) + 57/(-171). Let w(a) = -19*a**2 - 55*a + 6. Let p be w(f). Solve p*v - 16/7*v**2 - 4/7*v**3 + 0 = 0 for v.
-4, 0
Let k(a) be the first derivative of 5*a**3/12 - 35*a**2/4 + 65*a/4 + 5635. Factor k(g).
5*(g - 13)*(g - 1)/4
Let o(z) = 23 - 11*z**3 - 65*z**2 + 30*z + 8 + 33 + 4*z**3 + 9*z**3. Let n be o(32). Factor 2/5*k**5 - 8/5*k**3 + 4/5*k**4 + n*k - 16/5*k**2 + 0.
2*k**2*(k - 2)*(k + 2)**2/5
Let w be 2 + (-2 - 45) - 9/3. Let y = w - -53. Factor -6*u**3 - u**3 + 110*u**y + 5*u**4 + 3*u**2 - 111*u**5.
-u**2*(u - 3)*(u - 1)**2
Factor -10589*o**2 + 10585*o**2 + 1442*o - 155*o - 222784 + 601*o.
-4*(o - 236)**2
Suppose -7*b - 7 = -0. Let g be b/((12/(-9))/4). Factor -417 + 417 + 6*h**g + 2*h**3 - 20*h**5 + 12*h**4.
-4*h**3*(h - 1)*(5*h + 2)
Suppose 10 + 27/5*o - 1/5*o**3 - 24/5*o**2 = 0. Calculate o.
-25, -1, 2
Let m(v) be the third derivative of v**5/12 - 85*v**4/24 - 95*v**3/3 + 37*v**2 + 32. Factor m(i).
5*(i - 19)*(i + 2)
Factor -284 - 2/3*x**2 - 854/3*x.
-2*(x + 1)*(x + 426)/3
Let y(f) be the second derivative of f**4/84 + 33*f**3/2 + 346*f**2/7 + 4361*f. Let y(z) = 0. Calculate z.
-692, -1
Factor 82/19*b**2 - 880/19*b - 2/19*b**3 + 800/19.
-2*(b - 20)**2*(b - 1)/19
Let t(l) be the second derivative of -l**5/50 - 13*l**4/30 + 64*l**3/15 - 68*l**2/5 + 3*l - 8. Solve t(y) = 0 for y.
-17, 2
Let f(k) be the second derivative of -k**5/50 + 1023*k**4/10 - 1046529*k**3/5 + 1070599167*k**2/5 + 3925*k. Solve f(d) = 0 for d.
1023
Let k(j) be the second derivative of j**7/105 + 7*j**6/60 + 7*j**5/15 + 2*j**4/3 + 21*j**2 + 3*j + 25. Let g(m) be the first derivative of k(m). Factor g(z).
2*z*(z + 1)*(z + 2)*(z + 4)
Let v(d) be the first derivative of d**2 - 5*d - 1. Let t be v(5). Let t*o**3 + 3*o**3 - 3*o**3 + 0*o - 5*o = 0. Calculate o.
-1, 0, 1
Let t be ((-21)/6 - -4) + 59/2. Let y = -25 + t. Determine c so that -2 - y*c + c**2 + 2*c + 2*c = 0.
-1, 2
Let x(y) be the third derivative of 2*y**7/105 - 414*y**6/5 + 771282*y**5/5 - 159655374*y**4 + 99145987254*y**3 - 3850*y**2. Solve x(b) = 0.
621
Let a(w) be the second derivative of 4 - 4*w - 5/4*w**5 - 60*w**3 + 50*w**2 + 95/4*w**4. Factor a(t).
-5*(t - 10)*(t - 1)*(5*t - 2)
Let b(c) be the third derivative of c**5/20 - 55*c**4/8 - 28*c**3 - 599*c**2. Factor b(s).
3*(s - 56)*(s + 1)
Factor -41*f**2 + 552*f**2 + 160*f**3 + 560*f + 5*f**4 + 69*f**2.
5*f*(f + 2)**2*(f + 28)
Let i be 9/(-27) - -1 - (-32)/(-12). Let t be i - ((-22)/110 - 64/30). Solve t*f**2 + 1/6*f**3 - 1/3 - 1/6*f = 0.
-2, -1, 1
Let h = -13929 + 69961/5. Let k = h - 314/5. Factor -6/5*d**2 + 2/5*d**3 + 6/5*d - k.
2*(d - 1)**3/5
Let d(v) be the first derivative of v**6/40 + v**5/4 - v**4/8 - 5*v**3/2 + 71*v**2/2 - 104. Let u(k) be the second derivative of d(k). Factor u(j).
3*(j - 1)*(j + 1)*(j + 5)
Let g(i) be the first derivative of -i**3/3 - 209*i**2/2 + 852*i + 13321. Factor g(f).
-(f - 4)*(f + 213)
Let l(r) be the first derivative of -r**5/60 - 11*r**4/24 - 5*r**3/3 - 3*r**2 + 6*r - 2. Let f(m) be the second derivative of l(m). Find u such that f(u) = 0.
-10, -1
Factor -3/2*n - 9/4 - 1/4*n**2.
-(n + 3)**2/4
Factor 57161*f - 8 - 800*f**2 - 111704*f + 56147*f.
-4*(f - 2)*(200*f - 1)
Factor -1269*a + 536787/2 + 3/2*a**2.
3*(a - 423)**2/2
Let q be 2100/(-225) - (1 + -11). Let w(p) be the third derivative of 0*p + 1/12*p**6 + 0 + q*p**3 - 5/12*p**4 + 3*p**2 - 1/15*p**5. Solve w(h) = 0.
-1, 2/5, 1
Factor 130 - 14*l**3 - 290*l + 120*l**2 + 802*l - 2*l**4 - 2821 + 131.
-2*(l - 5)*(l - 4)*(l + 8)**2
Suppose -123*j = -150*j - 190*j. Let h(w) be the second derivative of j - 1/30*w**4 - 11*w - 4/15*w**3 - 3/5*w**2. Factor h(m).
-2*(m + 1)*(m + 3)/5
Let g(y) be the third derivative of y**6/6 - y**5/15 - 7*y**4/3 - 16*y**3/3 + 7*y**2 - 65*y. Factor g(h).
4*(h - 2)*(h + 1)*(5*h + 4)
Suppose -49*g - 18139 = 36349. Let y = 4449/4 + g. Solve 9/4*n**2 + y*n**4 - 5/4*n**3 + 1/2 - 7/4*n = 0.
1, 2
Let a be 30/20*10/12. Let k be 4 + 2*(-9 + 8). What is q in 3/2 + 1/4*q**k + a*q = 0?
-3, -2
Factor -801/2*r**2 + 3/2*r**3 + 0*r + 0.
3*r**2*(r - 267)/2
Let j(q) = -220*q**2 - 663 + 1379 - 25*q**4 - 651 + 180*q**3. Let g(f) = 6*f**4 - 45*f**3 + 55*f**2 - 16. Let x(h) = -15*g(h) - 4*j(h). What is n in x(n) = 0?
-1/2, 1, 2
Let b(i) = -6*i**2 + 73*i + 68. Let m be b(13). Let f(p) be the first derivative of -1/40*p**5 - p + 42 + 1/32*p**4 + 1/4*p**m - 1/4*p**2. Factor f(a).
-(a - 2)**2*(a + 1)*(a + 2)/8
Let c(o) = 14*o**2 + o + 1. Let x(f) = -155*f**2 + 22*f - 241. Let y(n) = 22*c(n) + 2*x(n). Determine i, given that y(i) = 0.
10, 23
Let z(i) be the first derivative of i**4/14 - 20*i**3/21 + 12*i**2/7 - 25*i + 10. Let b(d) be the first derivative of z(d). What is a in b(a) = 0?
2/3, 6
Factor 2/9*v**5 - 9234*v**2 + 666*v**3 + 43740*v - 182/9*v**4 + 0.
2*v*(v - 27)**3*(v - 10)/9
Let z be 2584/16150*100/8. Determine k so that 0 + 22/7*k**z + 18/7*k**4 + 6*k**3 + 0*k - 2/7*k**5 = 0.
-1, 0, 11
Let w(g) be the first derivative of -g**6/30 + g**5/25 + 13*g**4/20 - g**3/15 - 6*g**2/5 - 3659. Solve w(c) = 0 for c.
-3, -1, 0, 1, 4
Let x(c) = -11*c**5 + 30*c**4 - 35*c**3 - 48*c**2 + 40*c + 6. Let w(t) = t**5 + 3*t**2 - 1. Let a(z) = -6*w(z) - x(z). Determine h so that a(h) = 0.
-1, 0, 1, 2, 4
Let l(t) = -t**2 - 7*t - 2. Let g(j) = j**2 + 12*j + 3. Let b be g(-12). Let d(q) = -q**2 - 6*q - 3. Let x(c) = b*l(c) - 2*d(c). Factor x(a).
-a*(a + 9)
Let n(j) be the first derivative of 3/5*j**5 - 46 + 0*j**2 + 0*j + 9/4*j**4 + 2*j**3. Find d such that n(d) = 0.
-2, -1, 0
Suppose 3*n + 3*d = 2*n - 10, 0 = 4*d + 16. Determine t so that -106 + 106 - 2*t**3 + 24*t + 6*t**n - t**3 = 0