- 210*m**3 + 410*m - 3500*m**4.
5*m*(m - 41)*(m - 2)*(m + 1)
Let j(h) be the third derivative of h**5/160 + 121*h**4/16 + 483*h**3/16 - h**2 + 475*h + 3. Factor j(y).
3*(y + 1)*(y + 483)/8
Let c(z) = -z**3 - 15*z**2 - 14*z + 20. Let t be c(-14). Suppose o - t + 17 = 0. Factor 4*p**4 + 24*p**2 - 18 + 16*p + 16*p**o - 11 + 33.
4*(p + 1)**4
Suppose -3*y = -12*y + 27. Let h be -6 - (1 - 2 - 18/y). Factor -3/2*u + 0*u**2 + 1/2*u**3 - h.
(u - 2)*(u + 1)**2/2
Let g(l) be the third derivative of 24*l**2 + 1/15*l**5 + 18050/3*l**3 + 3*l + 95/3*l**4 + 0. Solve g(o) = 0.
-95
Let q = 898 + -22448/25. Let m(k) be the first derivative of 1/2*k**4 + 6/5*k**3 - 13 + 7/5*k**2 + q*k**5 + 4/5*k. Factor m(a).
2*(a + 1)**3*(a + 2)/5
Factor -5869*k**3 - 585 + 133*k + 302*k - 95*k**2 + 5874*k**3.
5*(k - 13)*(k - 3)**2
Let z(h) be the third derivative of -h**7/1785 + 37*h**6/1020 - h**5/15 - 6*h**4/17 - 367*h**2. Find x, given that z(x) = 0.
-1, 0, 2, 36
Let g(x) be the first derivative of -x**6/900 - 17*x**5/100 + 13*x**4/15 + 17*x**3 - 213. Let h(s) be the third derivative of g(s). Factor h(y).
-2*(y - 1)*(y + 52)/5
Let y(v) be the third derivative of -v**8/90720 + v**7/3240 + v**6/180 + 17*v**5/10 + 12*v**2. Let q(n) be the third derivative of y(n). Factor q(b).
-2*(b - 9)*(b + 2)/9
Let a(n) be the second derivative of -n**5/70 - 97*n**4/42 - 329*n**3/3 + 343*n**2 + 2*n + 22. Factor a(k).
-2*(k - 1)*(k + 49)**2/7
Let i be (-16 - -10)/((-27)/(-36)*-4). Let b(d) be the first derivative of 32/3*d + 7 - 3/4*d**4 + 74/9*d**3 - 80/3*d**i. Factor b(h).
-(h - 4)**2*(9*h - 2)/3
Suppose 0 = 2*c - 10*c + 160. Factor -c*w**2 - 5*w**3 - 24*w + 5*w**4 + 16*w + 28*w.
5*w*(w - 2)*(w - 1)*(w + 2)
Let d = 1338726 + -1338721. Solve 0 + 0*o + 0*o**2 - 1/4*o**d - 3/4*o**3 + o**4 = 0.
0, 1, 3
Let l(d) be the third derivative of -d**7/210 - 5*d**6/12 + 59*d**5/60 + 33*d**4/2 - 102*d**3 + 8091*d**2. Solve l(t) = 0.
-51, -3, 2
Let k(o) = -o - 47. Let l be k(-59). Suppose 8 = 28*n - 27*n - 3*s, -5*n + s = -l. Let 2/5*j**n + 72/5 - 24/5*j = 0. Calculate j.
6
Let l be (168795/(-2860) - -59)/((-3)/144). Find q such that 14/13*q**2 + 0 + l*q + 0*q**3 - 2/13*q**4 = 0.
-2, -1, 0, 3
Let u(t) = 3*t**3 - 2*t**2 + 16*t + 9. Let d be u(-7). Let v = -4919/4 - d. Factor v*j**4 - 45*j + 81/4 + 59/2*j**2 - 5*j**3.
(j - 9)**2*(j - 1)**2/4
Suppose 10*b - 294 + 54 = 0. Let u be 2 + 0 - 8/b. Suppose 5/3*o**3 - 1/6 + 5/6*o - u*o**2 + 1/6*o**5 - 5/6*o**4 = 0. What is o?
1
Let j(l) be the first derivative of -106 + 0*l - 105/2*l**2 + l**3. Find d such that j(d) = 0.
0, 35
Let p(k) be the first derivative of 2*k + 28 + 3/2*k**2 + 1/3*k**3. What is z in p(z) = 0?
-2, -1
Let z(m) be the third derivative of 7*m**4/24 - 62*m**3/3 - 2*m**2 + 31*m. Let l be z(18). Let 4/11 - 34/11*v - 56/11*v**3 + 86/11*v**l = 0. What is v?
1/4, 2/7, 1
Suppose 0 = -5*b + 5*x - 4955, -213 = 3*b + 4*x + 2753. Let j be 12*(-312)/b - (-6)/(-33). Solve -2*d + j*d**3 + 2/5 + 6/5*d**2 = 0 for d.
-1, 1/3
Suppose -670 = 2153*u - 2151*u. Let l = u + 337. Factor 2/19*g**l - 2/19*g + 0.
2*g*(g - 1)/19
Let 352 - 30*j - 1189*j - 141*j + 1010 + 0*j**2 - 2*j**2 = 0. Calculate j.
-681, 1
Let c(n) be the first derivative of -3*n**8/3920 + n**7/5880 - 139*n**3/3 - 185. Let w(d) be the third derivative of c(d). Factor w(m).
-m**3*(9*m - 1)/7
Let f(z) be the second derivative of z**5/120 - z**4/18 - z**3/12 + 3*z**2/2 + 1037*z. Factor f(n).
(n - 3)**2*(n + 2)/6
Let y(i) = -7*i**3 - 11*i**2 - 6*i - 12. Let m be y(-8). Factor -71*x + 99*x + 114*x + 4 + m*x**2 + 74*x.
4*(27*x + 1)**2
Let f(k) be the first derivative of 2*k**6/3 - 44*k**5/5 + 18*k**4 + 8*k**3/3 - 38*k**2 + 36*k - 736. Factor f(w).
4*(w - 9)*(w - 1)**3*(w + 1)
Let u(t) be the third derivative of -t**7/525 - t**6/75 + 63*t**5/25 + 81*t**4 + 5589*t**3/5 + 141*t**2 + 6*t. Factor u(z).
-2*(z - 23)*(z + 9)**3/5
Let l(k) be the second derivative of 2*k**7/21 - 4*k**5/5 + 2*k - 24. Factor l(g).
4*g**3*(g - 2)*(g + 2)
Suppose z = -4*u - 9, 0 = 5*u - 4*z - 73 - 5. Solve 2 + 5/3*y - 1/3*y**u = 0.
-1, 6
Let s(l) be the first derivative of 1/5*l**2 - 1/10*l**4 - 70 + 0*l + 0*l**3. Factor s(w).
-2*w*(w - 1)*(w + 1)/5
Let u be (5002/(-943) - -38) + -32. Factor -162/23*t**4 + 0 - 252/23*t**3 - u*t + 136/23*t**2.
-2*t*(t + 2)*(9*t - 2)**2/23
Let d(n) be the first derivative of -847*n**5/5 + 2255*n**4/4 - 2188*n**3/3 + 462*n**2 - 144*n + 3357. Suppose d(c) = 0. Calculate c.
6/11, 4/7, 1
Let 1/5*n**2 - 1/5*n - 42/5 = 0. Calculate n.
-6, 7
Let w(j) be the third derivative of j**5/20 - 55*j**4/8 + 168*j**3 + 13*j**2 + 51*j. Suppose w(a) = 0. What is a?
7, 48
Let c be (-60)/(-90) - 62/120. Let g(y) be the first derivative of 2 + c*y**4 - 75*y - 3*y**3 + 45/2*y**2. Factor g(p).
3*(p - 5)**3/5
Factor -1/3*v**4 + 0*v**3 + 0 + 256/3*v**2 + 0*v.
-v**2*(v - 16)*(v + 16)/3
Let t(c) be the second derivative of -c**5/60 - 13*c**4/12 - 44*c**3/3 + 1210*c**2/3 - 8326*c. Factor t(l).
-(l - 5)*(l + 22)**2/3
Suppose 0 = 10*a - 219 - 101. Factor 256*i + 120*i**2 - 47*i**4 - 3*i**5 + 144 - 16*i + a*i**4.
-3*(i - 3)*(i + 2)**4
Let v = 958583/14 + -136937/2. Solve -v - 1/7*a + 1/7*a**2 = 0.
-3, 4
Let k(y) be the first derivative of 0*y - 30 + 92*y**2 + 100/3*y**3 + y**4. Factor k(f).
4*f*(f + 2)*(f + 23)
Let -18750*p - 35562*p - 15376 - 1740*p**2 - 34495*p**3 + 34481*p**3 = 0. What is p?
-62, -2/7
Let s(z) be the first derivative of -3*z**5/25 - 39*z**4/20 + 37*z**3/5 + 327*z**2/10 + 36*z + 15948. Solve s(f) = 0.
-15, -1, 4
Suppose 0*o = 2*o + 3*q, 5*q = o - 13. Let g be (55/(-33))/(2/(-6)). Suppose -4*x**2 - 1614*x**o + 1609*x**3 - x**2 + g*x + 5 = 0. What is x?
-1, 1
Let a(z) = 56*z + 226. Let l(j) = 2*j**2 + 11*j - 10. Let s be l(-6). Let p be a(s). Factor -2/19*m**p + 0 + 2/19*m.
-2*m*(m - 1)/19
Let m = -158621 + 158625. What is g in -2/9*g**5 + 4/9*g - 2/3*g**2 + 2/3*g**m + 0 - 2/9*g**3 = 0?
-1, 0, 1, 2
Let g = -104558 + 522792/5. Factor -44/5*a + g*a**3 - 2*a**2 - 32/5.
2*(a - 8)*(a + 1)*(a + 2)/5
Let p(w) be the first derivative of -w**6/2880 - w**5/480 - 7*w**3/3 + 2*w - 78. Let i(j) be the third derivative of p(j). Factor i(d).
-d*(d + 2)/8
Let b(j) be the first derivative of 18*j + 0*j**2 + 13 + 3/100*j**5 + 2/5*j**4 + 8/5*j**3. Let u(a) be the first derivative of b(a). Factor u(v).
3*v*(v + 4)**2/5
Let b(l) = 4 - 3*l**3 - 528*l + 526*l + 2*l**3. Let z be b(0). Factor -3 - 20*a - 9 - z*a**2 - 3 - a**2.
-5*(a + 1)*(a + 3)
Solve 36*m + 4*m**2 + 13 + 2*m + 33*m + 155 + 21*m = 0.
-21, -2
Let m(k) = -k**3 - 14*k**2 - 52*k - 20. Let h be m(-6). Find u such that -4*u**2 + 21*u + u**2 + 30 + 5*u**2 + 5*u**2 - h*u**2 = 0.
-5, -2
Suppose 2*v = -3*v + 10. Suppose -a - 5*j = 70, -108 = -a + 5*j - 38. Factor -1/3*f**3 + a - 2/3*f**v + 0*f.
-f**2*(f + 2)/3
Let a be 5 - (-20)/8*12/10. Let v be (4 - 195/72) + 3/a. Solve 0*b**2 - 5/3*b + v*b**3 + 0 = 0.
-1, 0, 1
Let 0*t**2 + 8*t**2 - 30 + 4*t**2 - 18*t**2 + 17*t + 5*t**2 = 0. What is t?
2, 15
Let u be (-54)/(-3) + (-20184)/1131. What is q in 4/13*q**4 - 12/13 + u*q**5 - 12/13*q**3 - 40/13*q**2 - 38/13*q = 0?
-2, -1, 3
Let z = 1277835/8 + -159728. Factor -5/4 + z*d - 1/8*d**2.
-(d - 10)*(d - 1)/8
Suppose 1804*z + 270 = 1939*z. Factor 20/7*f**z - 44/7*f + 12/7*f**3 + 12/7.
4*(f - 1)*(f + 3)*(3*f - 1)/7
Let p(c) be the second derivative of c**4/4 - 15*c**3 - 93*c**2/2 + 971*c. Find y, given that p(y) = 0.
-1, 31
Let a(o) = 7*o**3 - 102*o**2 + 55*o - 25. Let s(g) = g**3 - 9*g - 5. Let n(t) = a(t) - 5*s(t). Determine w, given that n(w) = 0.
0, 1, 50
Let i = -2710756/167 - -16232. Let a = i - -704/501. Determine x, given that -2/3 - a*x**3 + 0*x**2 + 2/3*x**4 + 4/3*x = 0.
-1, 1
Let s(q) be the first derivative of -q**4/12 - 53*q**3/9 - 25*q**2/3 + 104*q/3 + 4843. Find j such that s(j) = 0.
-52, -2, 1
Let c(x) = -x + 5. Let s be c(6). Let r be (-41 - -47)*s/(-3). What is u in 5/2*u - 1/2*u**2 - r = 0?
1, 4
Find p such that -1/4*p**2 + 1/4*p**3 - 35 - 19*p = 0.
-7, -2, 10
Suppose 0 = 21*x - 68 + 5. Factor -2*w**x + 4*w**2 + 15*w - 2*w**4 - 15*w.
-2*w**2*(w - 1)*(w + 2)
Suppose -40*o + 103 + 29 = -28. Let t(u) be the third derivative of 6*u**2 + 1/4*u**5 + 0*u - 8/105*u**7 + 0 + 0*u**3 - 1/12*u**o - 1/5*u**6. Factor t(j).
-j*(j + 2)*(4*j - 1)**2
Find f, given that -24 + 101*f**3 + 643/5*f - 1