 59*w + 0*w**2 + 8/45*w**6 - 32/9*w**3 - 7*w**4. Factor k(s).
4*s*(s - 16)*(2*s + 1)**2/3
Let t(s) be the third derivative of -s**8/2940 + s**7/210 - 11*s**6/630 + s**5/42 + 67*s**3/6 + s**2. Let c(u) be the first derivative of t(u). Factor c(h).
-4*h*(h - 5)*(h - 1)**2/7
Let j = -943/10 - -2241531/23770. Let p = j - -4740/16639. Suppose -p*v**2 - 6/7*v + 0 = 0. Calculate v.
-3, 0
Let a be (-27)/54 + 10/((-560)/(-484)). Factor 27/7 + a*v + 33/7*v**2 + 3/7*v**3.
3*(v + 1)**2*(v + 9)/7
Suppose -5*u - 34 = 4*i - 6, -7 = 3*u + 17. Determine g, given that 71/2*g**2 + 6*g**4 - 4 - 5*g - 65/2*g**i = 0.
-1/4, 2/3, 1, 4
Let f(p) be the first derivative of -p**4/3 + 212*p**3/3 - 210*p**2 + 628*p/3 - 1180. Factor f(b).
-4*(b - 157)*(b - 1)**2/3
Factor 15/2*q**3 - 11/2*q**4 - 29*q + 31/2*q**2 - 1/2*q**5 + 12.
-(q - 1)**3*(q + 2)*(q + 12)/2
Let b(g) = 36*g**3 - g**2 + 2. Let y(w) = 325*w**3 + 91*w**2 - 204*w + 18. Let t(h) = -18*b(h) + 2*y(h). Factor t(o).
2*o*(o - 2)*(o + 102)
Solve -224 + 57*f**3 + 61*f**3 - 70*f**2 - 2776 + 1075*f - 186*f**3 + 63*f**3 = 0.
-24, 5
Let k(f) be the third derivative of 8*f**7/315 - 13*f**6/30 - 106*f**5/45 - 4*f**4/3 + 2772*f**2. Suppose k(c) = 0. Calculate c.
-2, -1/4, 0, 12
Let n(j) be the first derivative of -1/4*j**4 - 8 - 1/2*j**2 + 3/20*j**5 - 1/40*j**6 + 0*j**3 + 0*j. Let s(t) be the second derivative of n(t). Factor s(v).
-3*v*(v - 2)*(v - 1)
Suppose -37*c + 41*c + 49*c = -83*c. Let i(u) be the third derivative of 1/45*u**5 + 0*u + 2/9*u**4 + 11*u**2 + c + 8/9*u**3. Factor i(j).
4*(j + 2)**2/3
Let b be 12/(-20) - (-56)/10. Factor -36*k**b + 33*k**5 - 23*k**3 + 12*k**2 + 15*k**4 - k**3.
-3*k**2*(k - 2)**2*(k - 1)
Let w(f) be the second derivative of 1/135*f**6 + 2*f - 68/9*f**2 + 17/18*f**4 + 2/9*f**5 + 8 - 4/27*f**3. Find r such that w(r) = 0.
-17, -2, 1
Let u(t) = -t**3 + t**2 + 10*t + 414. Let l be u(0). Factor 207*o**3 + 208*o**3 + 4*o - 5*o + 18*o**2 - l*o**3 - 18*o.
o*(o - 1)*(o + 19)
Let m(j) be the third derivative of -j**5/660 + 65*j**4/22 - 25350*j**3/11 - 1241*j**2. Find s such that m(s) = 0.
390
Let q(l) be the second derivative of 2*l**7/21 + 388*l**6/15 - 2*l**5/5 - 388*l**4/3 + 2*l**3/3 + 388*l**2 + 1862*l. Suppose q(v) = 0. Calculate v.
-194, -1, 1
Suppose -3*a = -x + 32 - 140, -3*x = 3*a + 324. Let b = x - -110. Factor 7*l**2 - 6*l**b + 4*l**2 - 40 + 5*l - 15*l.
5*(l - 4)*(l + 2)
Solve 2*c**2 + 2072 - 7*c**2 - 92*c - 1352 + 23*c + 419*c = 0 for c.
-2, 72
Let k(u) = -20*u - 197. Let s be k(-10). Factor -5*r**2 - 5 - 3*r**5 - 23*r**s + 15*r - 5*r**2 + 13*r**3 + 15*r**4 - 3*r**5 + r**5.
-5*(r - 1)**4*(r + 1)
Let t(q) be the third derivative of -q**8/336 - 17*q**7/210 - 3*q**6/4 - 89*q**5/30 - 149*q**4/24 - 15*q**3/2 - 4*q**2 + 3*q. Factor t(l).
-(l + 1)**3*(l + 5)*(l + 9)
Let l(c) be the third derivative of -c**7/1785 - c**6/1020 + c**5/102 - c**4/68 - 1785*c**2. Determine w, given that l(w) = 0.
-3, 0, 1
Let z be (-392)/(-56) + (-13)/4. Let y = 27/7 - 87/28. Factor -z + y*w**2 + 3*w.
3*(w - 1)*(w + 5)/4
Suppose 0 = 2*z + 8, 2444*m - 4 = 2440*m - 3*z. Solve -12/5 + 4/5*o**m - 24/5*o**2 + 0*o**3 + 32/5*o = 0.
-3, 1
Let f be (-144)/(-6) - -4 - (5 + 0). Suppose -23 = 11*s - f. Find x, given that 0 + 5*x**3 + 5/2*x**4 + s*x - 15/2*x**2 = 0.
-3, 0, 1
Let w = -1186/685 + -4/2055. Let g = w - -239/60. Factor 3/8*p**2 + g*p + 15/8.
3*(p + 1)*(p + 5)/8
Let k(h) be the third derivative of h**5/300 + 131*h**4/30 - 35*h**3/2 - 3986*h**2. Let k(b) = 0. Calculate b.
-525, 1
Suppose -150 + 1/3*r**2 - 7/3*r = 0. What is r?
-18, 25
Let r(t) be the second derivative of t**8/6720 - t**7/420 + t**6/72 - t**5/30 - 133*t**3/6 - 25*t. Let l(g) be the second derivative of r(g). Factor l(w).
w*(w - 4)*(w - 2)**2/4
Let c(w) be the first derivative of -36*w + w**3 - 3/2*w**2 - 18. Factor c(y).
3*(y - 4)*(y + 3)
Solve -1665/2 - 3/4*z**2 - 201/4*z = 0.
-37, -30
Determine r so that -4 + 5949*r**2 + 15086*r**3 + 4 + 8835*r**5 - 17604*r**5 + 8939*r**5 + 162*r + 3133*r**4 = 0.
-9, -2/5, -1/34, 0
Let k be (-91)/49 + (-1)/7. Let x be ((-490)/(-294))/(k/8 - -1). Factor -x - 2/9*o**2 - 14/9*o.
-2*(o + 2)*(o + 5)/9
Let z(f) = f**4 - f**3 - f**2 + 1. Let s(w) = -11*w**2 - 4*w**3 + w**2 - 7 + 7*w**2 + 8. Let l(i) = -s(i) + z(i). Determine t, given that l(t) = 0.
-2, -1, 0
Let d(g) be the second derivative of -279*g**4/4 + 13*g**3/6 + g**2/3 + 5*g - 288. Find i, given that d(i) = 0.
-2/93, 1/27
Let f(n) be the third derivative of 5*n**5/12 - 1405*n**4/12 + 560*n**3/3 + 47*n**2 - 2. Let f(j) = 0. What is j?
2/5, 112
Suppose 18/11*g - 1/11*g**2 + 19/11 = 0. What is g?
-1, 19
Solve 1070*y**2 + 343*y**2 + 122500*y + 2*y**3 - y**3 + 3*y**3 - 13*y**2 = 0.
-175, 0
Let m(k) be the first derivative of 28 + 9*k + 0*k**2 + 1/3*k**3 + 1/12*k**4. Let l(c) be the first derivative of m(c). Let l(z) = 0. Calculate z.
-2, 0
Let a be (-10)/6 - 7134/(-2952). Factor 0 - 3/2*k**2 + a*k**4 + 0*k + 3/4*k**3.
3*k**2*(k - 1)*(k + 2)/4
Let f(x) = 8*x**2 + 528*x - 2240. Let v be f(-70). Factor 0 + 1/3*n**5 + 0*n + 0*n**3 - 2/3*n**4 + v*n**2.
n**4*(n - 2)/3
Let j be ((-1)/3)/(19/(-228)). Determine l so that -4*l**3 + j*l**2 + 7*l**3 + 3*l**3 - 2*l**3 - 8*l = 0.
-2, 0, 1
Factor 72/17*v**2 + 214/17*v**3 + 0*v - 6/17*v**4 + 0.
-2*v**2*(v - 36)*(3*v + 1)/17
Let k be 3/(-36) + (-820)/(-240). Let q(m) be the first derivative of k*m**3 - 10*m - 5/2*m**2 + 16 + 5/4*m**4. What is g in q(g) = 0?
-2, -1, 1
Factor 5337*u - 577*u**3 - 498*u**3 - 8046 + 1072*u**3 - 876*u**2.
-3*(u - 3)**2*(u + 298)
Find a such that 128/3*a**2 + 14 + 380/9*a + 44/3*a**3 + 2/9*a**4 = 0.
-63, -1
Let n = -8681 + 8683. Let c(w) be the third derivative of 55/24*w**4 + 0 + 1/24*w**6 - 1/2*w**5 + 0*w - 5*w**3 + 28*w**n. Factor c(p).
5*(p - 3)*(p - 2)*(p - 1)
Let t(v) = -v**2. Let i(k) = -13*k**2 + 36*k + 15. Let d(p) = -27*p**2 + 73*p + 29. Let o(n) = -3*d(n) + 7*i(n). Let x(u) = -o(u) + 4*t(u). Factor x(f).
3*(f - 6)*(2*f + 1)
Let b be 80/(-12)*6/(-4). Factor 80*g**3 - 125*g**4 - 120*g**2 + b*g**3 + 104*g**3 + 31*g**3 + 20*g.
-5*g*(g - 1)*(5*g - 2)**2
Let g = -969 + 972. Factor -15*j - 24*j - g*j**3 - 28*j - 102*j**2 + 24*j - 56*j.
-3*j*(j + 1)*(j + 33)
Suppose -3628 + 4692 = 532*v. Suppose -4/3 + 38/9*y**v - 38/9*y - 8/9*y**3 = 0. What is y?
-1/4, 2, 3
Let s(r) = -12*r**3 + 5208*r**2 + 10468*r + 5184. Let t(n) = 4*n**3 - 1736*n**2 - 3489*n - 1729. Let x(h) = 5*s(h) + 16*t(h). Factor x(j).
4*(j - 436)*(j + 1)**2
Let g(z) be the first derivative of 5/6*z**6 + 0*z**5 + 205 - 90*z**3 + 0*z + 0*z**2 - 135/4*z**4. Factor g(i).
5*i**2*(i - 6)*(i + 3)**2
Find x such that 0 + 21/5*x**4 - 31974/5*x + 22557*x**2 - 3072/5*x**3 = 0.
0, 2/7, 73
Let o be 1*3/(-2)*-6. Let n be (6/o)/((-4)/(-18)). Factor -12*a**2 - 8*a**n - 3*a**2 + 4*a**5 + 4*a + 15*a**2.
4*a*(a - 1)**2*(a + 1)**2
Let y = 992796 + -8935162/9. Suppose y*j**3 - 14/9*j**2 + 0 + 20/9*j = 0. Calculate j.
0, 2, 5
Suppose -62 = -13*n - 10. Factor -8*k - 4*k - 9*k - n*k**2 + k.
-4*k*(k + 5)
Factor 24490*d + 65880 - 105*d**4 - 103*d**4 + 213*d**4 - 2544*d**2 + 8574*d**2 + 9530*d + 395*d**3.
5*(d + 6)**3*(d + 61)
Let x(a) be the third derivative of a**6/60 - 316*a**5/15 + 8215*a**4 + 134832*a**3 + 9776*a**2. Find g such that x(g) = 0.
-4, 318
Let p = 177094/2415 + 2/805. Let r = -425/6 + p. Factor 15 + r*x - 5/2*x**2.
-5*(x - 3)*(x + 2)/2
Let r = -337 + 339. Let o be (-8)/12 + (-55)/(-15). What is m in 1 - 8*m - 28*m**2 + 31*m**r + o = 0?
2/3, 2
Let i(b) be the first derivative of -1/8*b**6 + 82 - 1/10*b**5 - 3/8*b**2 - 1/2*b + 3/8*b**4 + 1/3*b**3. Determine a, given that i(a) = 0.
-1, -2/3, 1
Let w(m) be the third derivative of -m**7/5880 + m**6/1260 + m**5/105 + m**3/3 + 81*m**2. Let c(q) be the first derivative of w(q). Let c(v) = 0. What is v?
-2, 0, 4
Suppose 0 = n - 4*b - 160, -320 = -2*n - b - 4*b. Factor 460 - n*h**2 + 196*h + 12*h**3 - 216 - 292.
4*(h - 12)*(h - 1)*(3*h - 1)
Suppose -6*h = -8*h + 26. Suppose 16*i - 9 = h*i. Factor 8*a**i + 4*a**5 + a**2 - 3*a**2 - 2*a**2 + 12*a**4 - 4*a**2 - 12*a - 4.
4*(a - 1)*(a + 1)**4
Suppose -5*p + 2*l + 67 = 0, 71*p = 67*p - l + 77. Let -1/2*q**2 - p*q - 289/2 = 0. What is q?
-17
Let n(x) = 70*x**2 - 20*x + 8. Let q be n(3). Let k = 580 - q. Factor -2/13*b + 4/13*b**k + 2/13*b**3 - 4/13.
2*(b - 1)*(b + 1)*(b + 2)