40 - 455*t**4/16 - 114*t**3 - t**2 - 1112. Factor b(r).
3*(r - 456)*(r + 1)/2
Let n = 1561997 + -7809959/5. Factor 0 + 2/5*o**3 - 24/5*o**2 - n*o.
2*o*(o - 13)*(o + 1)/5
Let x(j) be the first derivative of j**4/4 + 20*j**3/3 + 11*j**2 + 59*j + 289. Let b be x(-19). Find g, given that 3/5*g - 6/5*g**b + 0 + 3/5*g**3 = 0.
0, 1
Let v(s) be the first derivative of -s**4/4 - 25*s**3/3 + 53*s**2/2 - 27*s - 2246. Factor v(g).
-(g - 1)**2*(g + 27)
Let n(x) be the third derivative of -x**7/210 - 29*x**6/120 - 257*x**5/60 - 451*x**4/24 + 363*x**3 - 867*x**2. Factor n(c).
-(c - 2)*(c + 9)*(c + 11)**2
Factor -329143 + 4*r**2 - 59*r + 658379 - 329012 - r.
4*(r - 8)*(r - 7)
Factor -1064/3*h**2 + 0 + 0*h - 2/3*h**3.
-2*h**2*(h + 532)/3
Let h(a) = -7*a**3 + 2*a**2. Let s(q) be the first derivative of 11*q**4/2 - 2*q**3 - 90. Suppose -11*o - 64 = -15*o. Let l(i) = o*h(i) + 5*s(i). Factor l(m).
-2*m**2*(m - 1)
Let t be (-600)/576*(-6)/(1 + 2). Let v(u) be the third derivative of -t*u**3 + 20*u**2 - 1/120*u**5 + 5/24*u**4 + 0 + 0*u. Factor v(k).
-(k - 5)**2/2
Let i = 447 + -445. Let s(b) = -3*b**4 - 6*b**3 + b**2 + 14*b - 6. Let n(l) = 7*l**4 + 13*l**3 - l**2 - 30*l + 11. Let r(k) = i*n(k) + 5*s(k). Factor r(h).
-(h - 1)**2*(h + 2)*(h + 4)
Let s = -31735/4 - -7934. Let d(p) be the second derivative of 3/20*p**5 + 0*p**6 + 0*p**2 - 6*p + 0*p**4 + 0 - 1/28*p**7 - s*p**3. Solve d(u) = 0.
-1, 0, 1
Let q(g) be the third derivative of -g**6/480 - 13*g**5/240 + 35*g**4/24 + 2960*g**2. Factor q(o).
-o*(o - 7)*(o + 20)/4
Let h(t) be the second derivative of -t**5/70 + 11*t**4/6 + t**3/21 - 11*t**2 - 1007*t - 1. Solve h(w) = 0 for w.
-1, 1, 77
Let d(n) be the first derivative of 2*n**3/9 - 116*n**2/5 - 56*n/3 + 2974. Factor d(a).
2*(a - 70)*(5*a + 2)/15
Let g(p) = 3*p**2 + 9*p - 4. Let r be g(-4). Determine n so that r*n**4 - 56*n + 18*n**3 + 54*n + 6*n**2 + 2*n**4 = 0.
-1, 0, 1/5
Let k(m) be the third derivative of m**6/540 + 4*m**5/45 - 109*m**4/108 + 28*m**3/9 - 648*m**2. Find s such that k(s) = 0.
-28, 1, 3
Factor -12*o**2 + 1563*o - o**3 - 535*o - 10 - 531*o - 518*o.
-(o + 1)**2*(o + 10)
Suppose -4*h = -20*h + 48. Solve -2*l**h - 61*l + 3*l**3 + l**4 + 0*l**2 - l**2 + 60*l = 0.
-1, 0, 1
Let n be (28/(-147))/((-32)/14). Let u(z) be the third derivative of 0 + 0*z + 5*z**2 + n*z**5 - 5/4*z**4 + 15/2*z**3. Let u(g) = 0. Calculate g.
3
Let p(w) be the first derivative of -w**6/360 - 41*w**5/60 - 1681*w**4/24 + 202*w**3/3 - 20. Let u(m) be the third derivative of p(m). Factor u(z).
-(z + 41)**2
Let r(b) = b**3 - 11*b**2 - 6*b - 68. Let y be r(12). Suppose -3*s**2 - y*s - 6*s**3 + s**2 + 2 + 6*s**3 + 4*s**3 = 0. Calculate s.
-1, 1/2, 1
Let v(m) be the first derivative of -4/3*m**3 + 10*m**2 - 16*m - 136. Factor v(x).
-4*(x - 4)*(x - 1)
Suppose 0 = -81*q + 80*q + 2. Let u be q/(-8) - 189/(-252). Solve -u*x + 3/4 - 1/4*x**2 = 0.
-3, 1
Find r, given that 48/17*r + 162/17*r**5 - 376/17*r**2 + 28*r**3 + 1062/17*r**4 + 0 = 0.
-6, -1, 0, 2/9
Let k(l) be the second derivative of l**7/420 - 43*l**6/900 + 2*l**5/25 - 7*l**3/6 - 3*l**2/2 + 47*l. Let v(z) be the second derivative of k(z). Factor v(a).
2*a*(a - 8)*(5*a - 3)/5
Let f = -2/3555 + 14933/3555. Let h(d) be the first derivative of -15/2*d**4 - 18 + 81*d + f*d**5 - 18*d**3 + 81/2*d**2 - 1/2*d**6. Factor h(z).
-3*(z - 3)**3*(z + 1)**2
Suppose -32/15*g**4 - 142/5 + 2384/15*g**3 + 3556/15*g - 8002/15*g**2 = 0. Calculate g.
1/4, 3, 71
Let a(v) be the second derivative of -4/9*v**2 + 1/54*v**4 + 43*v + 1/90*v**5 - 4/27*v**3 - 1. Let a(d) = 0. Calculate d.
-2, -1, 2
Let m(t) be the third derivative of t**5/450 - 71*t**4/90 + 56*t**3/9 + 13*t**2 - t - 2. Factor m(b).
2*(b - 140)*(b - 2)/15
Let x(h) be the third derivative of 0*h - 11/276*h**4 + 30*h**2 - 1/1380*h**6 - 2/23*h**3 + 0 - 1/115*h**5. Factor x(d).
-2*(d + 1)*(d + 2)*(d + 3)/23
Suppose 3 = 4*i + 5*f, 4*i - 10 = 6*f - 4*f. Let -25*h**3 - 10*h + 0*h + 7*h - 26*h**i - 4*h**4 - 2*h = 0. What is h?
-5, -1, -1/4, 0
Let o(m) = 9756*m + 107319. Let t be o(-11). Factor 1/3*r**2 - 10/3 + t*r.
(r - 1)*(r + 10)/3
Let z = -3/616 + 1247/3080. Let j(k) be the second derivative of 1/3*k**3 + 5/6*k**4 + 0 + z*k**5 + 28*k + 0*k**2. Factor j(x).
2*x*(x + 1)*(4*x + 1)
Let y(s) = -4*s - 2*s + 2 + 3*s + s. Let k be y(0). Factor -4*n - 6 + 0*n + 3*n**2 + 0*n - n**k.
2*(n - 3)*(n + 1)
Let u(w) be the third derivative of -w**7/630 + w**6/72 - w**5/20 + 7*w**4/72 - w**3/9 + w**2 - 687*w. Let u(i) = 0. Calculate i.
1, 2
Determine k, given that -26*k + 129/5 + 1/5*k**2 = 0.
1, 129
Let a = 28978 - 28978. Factor j**3 + 0*j**2 + 0 + 1/2*j**5 + a*j + 3/2*j**4.
j**3*(j + 1)*(j + 2)/2
Let h(o) be the third derivative of 0 + 0*o**5 + 0*o**3 + 17*o - 1/30*o**6 + 0*o**4 - 1/105*o**7 - 2*o**2. Solve h(v) = 0.
-2, 0
Factor -1/5*v**3 + 9/5*v**2 + 12/5 - 4*v.
-(v - 6)*(v - 2)*(v - 1)/5
Suppose -41 + 31 = -5*x. Factor -26 + 4102*t - 4130*t - 6*t**x + 4*t**2.
-2*(t + 1)*(t + 13)
Let b(z) be the first derivative of 35 - 2/27*z**3 + 4/9*z**2 + 0*z. Factor b(c).
-2*c*(c - 4)/9
Let v(r) = 14*r**2 - 206*r + 1108. Let f(b) = -9*b**2 + 137*b - 738. Let p(j) = -8*f(j) - 5*v(j). Find i, given that p(i) = 0.
7, 26
Let -85*b**3 + 22*b**3 + 16*b**3 + 22*b**3 + 84*b + 5*b**2 + 24*b**3 = 0. Calculate b.
-7, 0, 12
Let h = 8698 - 113068/13. Factor -h*k + 4/13 + 0*k**2 + 2/13*k**3.
2*(k - 1)**2*(k + 2)/13
Let h(r) be the second derivative of -r**6/288 + 7*r**5/32 - 16*r**3/3 + 31*r + 2. Let m(x) be the second derivative of h(x). Suppose m(f) = 0. What is f?
0, 21
Find a, given that 570 + 222 + 18*a**3 + 1212*a + 23*a**3 + 630*a**2 + 3*a**4 - 3*a**3 + 79*a**3 = 0.
-33, -2
Let z(i) = 8*i**2 + 8*i - 7. Let m(l) = -l**2 + 1. Let s(n) = -3*m(n) - z(n). Let g(a) = -16*a**2 - 24*a + 10. Let r(f) = -3*g(f) + 10*s(f). Factor r(w).
-2*(w - 1)*(w + 5)
Let a(i) be the third derivative of -i**6/2520 - 13*i**5/840 + 9*i**3/2 - 100*i**2. Let k(m) be the first derivative of a(m). Factor k(l).
-l*(l + 13)/7
Let p = -19314 + 96586/5. What is t in -4/5*t**5 + 8/5*t**4 - 4/5*t + 8/5*t**3 + 8/5 - p*t**2 = 0?
-1, 1, 2
Let n = -11357 - -34075/3. Suppose 0 = -2*f + 2*v + 18 - 6, 4*f = v + 18. Factor 8/3 + n*u**2 - f*u.
4*(u - 2)*(u - 1)/3
Let y(c) = 358*c**2 - 688*c - 54. Let p be y(2). What is m in 1/9*m**3 - 1/9*m + 34/9 - 34/9*m**p = 0?
-1, 1, 34
Suppose -4*u + 16 = -0*u. Suppose 0 = -13*w + 12*w + u. Factor -5*n**3 - 5*n**3 + 5*n**4 - w*n**4 + 4*n**4.
5*n**3*(n - 2)
Let h = 18/45037 + 180058/225185. Suppose -h*y**2 + 1/5*y**3 + 0 + 0*y = 0. What is y?
0, 4
Let c(i) be the second derivative of -i**7/168 + 41*i**6/60 - 1417*i**5/80 - 451*i**4/2 - 726*i**3 - 4435*i. Suppose c(u) = 0. What is u?
-3, 0, 44
Determine g, given that -28/11*g**2 - 54/11*g + 4/11 = 0.
-2, 1/14
Let p(q) be the second derivative of -q**6/135 - q**5/90 + 7*q**4/54 + q**3/27 - 2*q**2/3 + 2*q + 96. Suppose p(g) = 0. What is g?
-3, -1, 1, 2
Let a be (-30)/(-43 + 31 + -3). Factor 0*x - 5/2*x**4 - 25/4*x**a + 35/4*x**3 + 0.
-5*x**2*(x - 1)*(2*x - 5)/4
Suppose -31434*h = -31436*h. Let x(w) be the first derivative of 1/48*w**6 + 0*w**5 - 3 + 0*w**4 + h*w + 0*w**2 + 0*w**3. Factor x(q).
q**5/8
Let x(v) be the second derivative of v**4/28 + 27*v**3/14 + 27*v**2 + 146*v. Let x(f) = 0. Calculate f.
-21, -6
Let r(j) be the third derivative of -j**2 + 0*j**3 + 0*j + 29 - 7/144*j**4 - 1/360*j**5. Factor r(d).
-d*(d + 7)/6
Suppose 18*c - 29*c + 44 = 0. Suppose -4*w - h = -12, -2*w + c*h = 6*h - 12. Solve 0 - 2/3*f + 2/9*f**w = 0.
0, 3
Let a be ((-11)/(-2))/((-2)/(-4)). Suppose a*p - 5*p - 12 = 0. Factor 4 + 7*n**p - n**3 + 5 - 3*n - 12*n.
-(n - 3)**2*(n - 1)
Suppose 3468*x**4 + 2*x**5 + 422 - 422 + 172*x**3 - 3558*x**4 = 0. Calculate x.
0, 2, 43
Suppose 18 = n + 63. Let s be -1 - -3 - ((-168)/n)/2. Factor 0 - 4/5*d + s*d**2.
2*d*(d - 6)/15
Suppose y - 3662*b = -3658*b + 1314, -2*b - 1332 = -y. Suppose 18*n**2 + y + 270*n + 2/5*n**3 = 0. What is n?
-15
Suppose 4*o + 12*t - 10 = 11*t, 0 = -5*o + 4*t + 23. Let g(c) be the first derivative of -2/15*c**o + 0*c + 15 + 1/10*c**2. Factor g(m).
-m*(2*m - 1)/5
Suppose 3*o = o - 3*s - 27, 22 = -2*o - 2*s. Let k(p) = 2*p + 15. Let i be k(o). Factor 6*v**3 + 2*v**4 + 4*v**5 - 2*v**i - 10*v**4.
4*v**3*(v - 1)**2
Let h(s) be the third derivative of s**6/90