i**2 + 6/7*i - 2*i**x.
-2*i*(i + 1)*(7*i - 3)/7
Let a(n) be the third derivative of 0*n - 13/12*n**5 + 0 - 25*n**2 - 15/2*n**3 - 1/12*n**6 - 5*n**4. Suppose a(p) = 0. Calculate p.
-3, -1/2
Let m(d) be the third derivative of 11/270*d**6 - 125/2*d**3 + 0*d + 7/6*d**5 + 25/2*d**4 - 142*d**2 + 1/1890*d**7 + 0. Factor m(j).
(j - 1)*(j + 15)**3/9
Suppose 0 = -5*i - 15, -3*x - 3*i + i + 24 = 0. Suppose -2*l + x = -2*t, -7*t + 11*t + 25 = 5*l. Solve 1 + 5 - 50*p - 2*p**2 + 54*p + t*p**2 = 0.
-1, 3
Suppose 92*m = 180 + 372. Let b(r) be the second derivative of 12*r + 10/3*r**3 - 2*r**2 - 11/4*r**4 - 1/6*r**m + 0 + 11/10*r**5. Factor b(f).
-(f - 2)*(f - 1)**2*(5*f - 2)
Let r(a) be the third derivative of a**6/30 - 2*a**5/3 + 16*a**4/3 - 64*a**3/3 - 135*a**2 + 2*a. Factor r(d).
4*(d - 4)**2*(d - 2)
Let l be ((8 - -7) + -17)/((-2)/7). Let d be l + 1/(10/(-68)). Determine h, given that 3/5*h + 2/5*h**2 + d = 0.
-1, -1/2
Let c be ((-131225)/1267 - -103)/(1 - (-9)/(-7)). Factor 3/7*x**c + 72/7*x + 69/7.
3*(x + 1)*(x + 23)/7
Let y(i) be the third derivative of i**6/600 - 2*i**5/75 + i**4/6 - 8*i**3/15 - 7981*i**2. Factor y(t).
(t - 4)*(t - 2)**2/5
What is f in -16/3*f**5 + 256/3 + 3124/3*f**2 + 1712/3*f + 148/3*f**4 + 1526/3*f**3 = 0?
-4, -2, -1/2, -1/4, 16
Let m be ((-4)/(-3))/((10/(-66))/(-5)). Determine v so that -42*v**2 + 48*v**4 + 9*v**5 - 2 - m*v + 79*v - 44*v**3 - 6 + 2 = 0.
-6, -1, 1/3, 1
Let x(b) = -2*b - 1. Let m(o) = 7*o + 4. Let f(z) = 6*m(z) + 26*x(z). Let l be f(-1). Suppose -l*q + 72 + 2*q**2 + 17*q + 15*q = 0. Calculate q.
-6
Let d(b) be the first derivative of 0*b - 39 + 3/8*b**2 - 9/2*b**3. Factor d(q).
-3*q*(18*q - 1)/4
Let a(l) = 1. Suppose 0 = 2*j + 2*n + 3*n - 3, -2 = j - n. Let p(u) = -116*u - 4 - 4*u**3 + 8*u**2 + 4*u**2 + 104*u. Let g(q) = j*p(q) - 8*a(q). Factor g(c).
4*(c - 1)**3
Let s(n) be the third derivative of 5*n**8/336 - 19*n**7/14 - 59*n**6/8 - 179*n**5/12 - 25*n**4/2 - 2041*n**2 + 2. Factor s(p).
5*p*(p - 60)*(p + 1)**3
Let z(i) = -4*i**3 + 34*i**2 + 96*i - 128. Let x(u) = 21*u**3 - 168*u**2 - 483*u + 641. Let d(v) = 2*x(v) + 11*z(v). Factor d(l).
-2*(l - 21)*(l - 1)*(l + 3)
Solve 729600*d**3 + 4495*d**4 + 25*d**5 - 20*d**5 + d - 685*d**4 + 1444000*d**2 - d = 0 for d.
-380, -2, 0
Let f(j) be the second derivative of -j**4/4 - 86*j**3 - 513*j**2/2 - 5158*j. Determine c, given that f(c) = 0.
-171, -1
Let t(j) = 5*j**3 - 80*j**2 + 3. Let v be t(16). Factor 4/11*m + 2/11*m**2 + 0 - 2/11*m**v.
-2*m*(m - 2)*(m + 1)/11
Factor -1/4*s**2 + 0 + 9*s.
-s*(s - 36)/4
Let v(y) = -y**3 - 3*y + 1. Let g(h) = 15*h**3 - 36*h**2 - 549*h - 1662. Let f(t) = g(t) + 12*v(t). Factor f(o).
3*(o - 22)*(o + 5)**2
Let 704*i + 148/5*i**2 + 2/5*i**3 + 5440 = 0. What is i?
-34, -20
Let u(y) = y**3 + 10*y**2 + 64*y + 76. Let x(m) = m**2 - m - 1. Suppose 36*r = 92 + 88. Let q(l) = r*u(l) + 20*x(l). Factor q(d).
5*(d + 2)*(d + 6)**2
Let i(u) be the first derivative of -u**5/60 - u**4/24 + u**3 - 15*u**2/2 - 52. Let w(j) be the second derivative of i(j). Find m, given that w(m) = 0.
-3, 2
Let c(m) be the first derivative of 128*m**5/55 + 136*m**4/11 + 214*m**3/11 + 68*m**2/11 + 8*m/11 + 3708. Suppose c(v) = 0. Calculate v.
-2, -1/8
Let a be 33/7 + -5 - 2390/14. Let m = -129 - a. Determine h so that -m*h**4 + 44*h**4 - 4*h**3 + 4*h**3 - 6*h**2 + 4*h = 0.
-2, 0, 1
Let k(g) = 28*g**3 - 163*g**2 + 192*g + 57. Let x(f) = -3*f**3 + 18*f**2 - 21*f - 6. Let q(p) = -6*k(p) - 57*x(p). Suppose q(v) = 0. What is v?
0, 1, 15
Let f(m) = -2*m + 42. Let l be f(19). Factor l*c**2 + 2*c**3 - 11*c**4 + 24*c + 16 + 8*c**4 + c**4 - 8*c**3.
-2*(c - 2)*(c + 1)*(c + 2)**2
Let n be (-343)/49 + (-28)/4 + 11/((-99)/(-162)). Determine g, given that -315/4*g**2 - 219/4*g + 78*g**3 - 12*g**n - 15/2 = 0.
-1/4, 2, 5
Let m(x) be the second derivative of -x**9/60480 - x**8/13440 + x**7/2016 + x**6/480 - x**4/12 - 41*x. Let o(w) be the third derivative of m(w). Factor o(i).
-i*(i - 2)*(i + 1)*(i + 3)/4
Factor -360 + 906/5*k - 3/5*k**2.
-3*(k - 300)*(k - 2)/5
Suppose -y - 5*h = 5, 7*h - 3*h = -2*y + 8. Suppose 59*n = y*n - 14*n. Factor n*i + 4/9*i**2 - 4.
4*(i - 3)*(i + 3)/9
Let v(d) be the first derivative of 2*d**3/3 - 11*d**2/2 - 24*d - 42. Let l(r) = r**2. Let n(k) = 12*l(k) - 4*v(k). Factor n(u).
4*(u + 3)*(u + 8)
Let b(k) be the second derivative of 3*k**5/160 - 5*k**4/16 - 91*k**3/16 - 15*k**2 - 2328*k. Factor b(q).
3*(q - 16)*(q + 1)*(q + 5)/8
Factor 50*l**2 + 75*l - 235 - 51*l**2 - 20*l + 31.
-(l - 51)*(l - 4)
Let j(k) be the second derivative of k**7/11340 - 17*k**6/1620 - 7*k**5/108 + k**4/4 - k**3/6 - 11*k - 7. Let q(m) be the third derivative of j(m). Factor q(b).
2*(b - 35)*(b + 1)/9
Let g(y) be the first derivative of -4*y + 5 + 4/13*y**3 - 1/78*y**4 - 36/13*y**2. Let i(p) be the first derivative of g(p). Determine t so that i(t) = 0.
6
Suppose -3*c - 3 = -4*s, -c + 17747*s + 6 = 17748*s. Solve 0 - 3*u**c - 48/5*u - 3/5*u**4 + 66/5*u**2 = 0 for u.
-8, 0, 1, 2
Let k(c) = 9*c**2 - 7*c + 48. Let u be k(-19). Factor -324 - 3*q**3 + 27*q**2 + u*q - 6853*q + 3423*q.
-3*(q - 6)**2*(q + 3)
Solve 945/2 + 85*n - 5/2*n**4 - 470*n**2 - 85*n**3 = 0.
-27, -7, -1, 1
Let h(z) be the first derivative of 26*z**5/15 + 23*z**4/9 - 1550*z**3/27 - 142*z**2/9 + 80*z/9 + 1368. Let h(x) = 0. What is x?
-5, -1/3, 2/13, 4
Let k = -812 + 606. Let r = -206 - k. Factor 8/7*n + 20/7*n**2 + 8/7*n**3 + r.
4*n*(n + 2)*(2*n + 1)/7
Let v(q) = q**2 + 22*q - 29. Let y be v(-25). Let t be (y/69)/(1/4). Factor -4/3 + 6*g - t*g**2.
-2*(g - 2)*(4*g - 1)/3
Let c be ((-80)/(-4))/((-10)/(-5)). Let p(z) be the first derivative of 0*z**2 - c + 0*z + 0*z**3 + 1/10*z**4. Solve p(y) = 0.
0
Let i(b) = 8*b**2 + 23*b - 28. Let m(r) = 5*r**2 + 93 - 10 - 28*r**2 - 68*r. Let f(q) = 8*i(q) + 3*m(q). Solve f(s) = 0 for s.
-5, 1
Let u = 29981/9 + -3331. Let k(t) be the first derivative of -2/3*t + 1/6*t**4 + u*t**3 + 6 - 1/3*t**2. Factor k(y).
2*(y - 1)*(y + 1)**2/3
Let z be 35606/(-6559) + (8 - 0). Factor z*p + 16/7 + 2/7*p**2.
2*(p + 1)*(p + 8)/7
Suppose 0 = -2*i + 3 - 1. Suppose 17 = v + 5*l, -2*v + 2 = -l + i. Factor -v*u - 2*u**3 + 4*u + 0*u.
-2*u*(u - 1)*(u + 1)
Let c(h) be the second derivative of h**5/40 - 3*h**4/8 - h**3/3 + 9*h**2 + h + 1641. Factor c(w).
(w - 9)*(w - 2)*(w + 2)/2
Let b(j) be the second derivative of -j**7/294 + j**6/42 - 3*j**5/70 - j**4/21 + 4*j**3/21 + 1700*j. Factor b(a).
-a*(a - 2)**3*(a + 1)/7
Let q(a) = 5*a**2 + 416*a - 31. Let y(c) = -c + 1. Let u(m) = -q(m) + 4*y(m). Let n(g) = -g**2 - 70*g + 6. Let b(l) = 35*n(l) - 6*u(l). Factor b(x).
-5*x*(x - 14)
Suppose -11*t = -21 + 76. Let h(v) = -v**2 - 23*v + 10. Let k(b) = b**2 + 12*b - 5. Let f(m) = t*k(m) - 2*h(m). Factor f(j).
-(j + 5)*(3*j - 1)
Factor -192 + 132*k - 87*k + 767*k**2 - 771*k**2 + 151*k.
-4*(k - 48)*(k - 1)
Factor -95/2*f**2 + 5/4*f**4 + 175/4*f**3 - 90*f + 0.
5*f*(f - 2)*(f + 1)*(f + 36)/4
Suppose -5*c + 15 = 0, 142 = 2*x - 3*c - 825. Let s = -975/2 + x. What is t in 1/8*t**2 + 1/2*t + s = 0?
-2
Let g(y) be the third derivative of y**5/150 + y**4/10 + 8*y**3/15 - 208*y**2. Factor g(j).
2*(j + 2)*(j + 4)/5
Let v = 84199 - 84199. Factor -x**2 - 1/3*x**4 - 4/3*x**3 + 0*x + v.
-x**2*(x + 1)*(x + 3)/3
Let b = -1073 + 1072. Let v be (-120)/132*(b - 2/(-10)). Factor 0 + 2/11*j**3 + v*j**2 + 0*j.
2*j**2*(j + 4)/11
Suppose 5016 = -227*z + 215*z. Let s be (-1)/(5/8)*285/z. Factor -10/11*f**2 - 2/11*f**3 - s*f + 0.
-2*f*(f + 2)*(f + 3)/11
Let n(s) be the second derivative of -1/2*s**4 - 7/5*s**3 - 9/5*s**2 + 6*s - 3 - 3/50*s**5. Factor n(b).
-6*(b + 1)**2*(b + 3)/5
Let t = 5503/14 - 16495/42. Factor -2/3*j**2 - 1/3*j**3 + 2/3 + t*j.
-(j - 1)*(j + 1)*(j + 2)/3
Let c = 534 - 536. Let o be 25 - 29 - 9/c. Factor 1/8 + o*i + 1/8*i**4 + 1/2*i**3 + 3/4*i**2.
(i + 1)**4/8
Suppose -462*c - 48 = -478*c. Let b(w) be the third derivative of 0*w + 27*w**2 - 1/24*w**4 + 0 + 1/480*w**5 + 1/3*w**c. Determine o, given that b(o) = 0.
4
Let b(g) be the first derivative of 2*g**3/15 + 116*g**2/5 + 896*g/5 - 10672. Factor b(q).
2*(q + 4)*(q + 112)/5
Let z = -611 + 613. Factor 312 + 231 + 88*i - 740 + z*i**2 + 283.
2*(i + 1)*(i + 43)
Let w be 108108/27036 - -1*2*-2. Let r = w - -2258/3755. What is h in -3/5*h**5 - 6/5*h + 0 + 9/5*h**3 + r*h**4 - 3/5*h**2 = 0?
-1, 0,