5 - 16/21*k**3 + 10. Factor a(m).
-2*m*(m + 1)*(m + 2)**2/7
Let l(d) be the second derivative of d**5/70 + 293*d**4/42 + 583*d**3/21 + 291*d**2/7 - 2286*d. Factor l(x).
2*(x + 1)**2*(x + 291)/7
Let h = -1979811 + 1979813. Determine v, given that 44/9*v - 10/9*v**h + 10/3 = 0.
-3/5, 5
Let a = -13157 - -13159. Let p(v) be the second derivative of -25/112*v**7 + 0 - v**6 - 1/2*v**4 - 19*v + 0*v**3 + 0*v**a + 57/40*v**5. Factor p(t).
-3*t**2*(t + 4)*(5*t - 2)**2/8
Let n = -160 - -159. Let v be (8 - 69/9) + 1 + n. Factor 2/3*b + 0 - v*b**2.
-b*(b - 2)/3
Determine s, given that 6*s**3 - 30*s**3 + 4253*s**5 - 120*s**3 + 45*s**4 - 4252*s**5 = 0.
-48, 0, 3
Let -20168*r**4 + 24*r**3 + 2*r**5 + 10086*r**4 + 56*r**2 + 10052*r**4 = 0. Calculate r.
-1, 0, 2, 14
Suppose -x**3 - 189*x**2 - 155922 - 94125 - 9077*x + 965*x - 5013*x + 1218*x = 0. What is x?
-63
Suppose 6*g + 210 = 3*g. Let a = g - -75. Factor 5*h**2 - 2*h**3 - h**4 - 4*h**2 + 3*h**4 - a*h**2.
2*h**2*(h - 2)*(h + 1)
Let m(s) be the first derivative of -52 + 20*s**2 + 4/3*s**3 - 44*s. Let m(t) = 0. What is t?
-11, 1
Let y(q) = q**2 + 5*q - 11. Let d be y(-7). Let u(r) = 3*r + 28. Let n be u(-8). Factor 4*o - 5*o**2 - 31*o**3 - 16*o**n + d*o**3 - 3*o**2.
-4*o*(o + 1)**2*(4*o - 1)
Let m(j) be the first derivative of -3/5*j**2 - 7/5*j + 1/15*j**3 + 77. Suppose m(z) = 0. What is z?
-1, 7
Let u(a) be the third derivative of 1/420*a**6 + 0 + 67*a**2 + 0*a**3 + 1/21*a**4 + 0*a - 2/105*a**5. Factor u(k).
2*k*(k - 2)**2/7
Let p be ((-472)/(-336) - 16/12)*6. Let g(f) be the first derivative of -1/7*f**3 - 4 - p*f - 3/7*f**2. Suppose g(b) = 0. Calculate b.
-1
Let r(y) be the third derivative of y**8/336 - y**7/21 + y**6/20 + 7*y**5/15 - 7*y**4/24 - 3*y**3 - 488*y**2. Let r(v) = 0. What is v?
-1, 1, 2, 9
Let o(x) be the second derivative of 3*x**4/4 - 107*x**3/6 + 44*x**2 + 3*x - 299. Factor o(u).
(u - 11)*(9*u - 8)
Let g be 14/4*(-48)/(-35). Let s be (-6)/30 + 4/(-6) + 1. Factor g + s*y**2 - 8/5*y.
2*(y - 6)**2/15
Let b(x) = -x**5 - 2*x**4 - x**3 - 10*x**2 + 6*x + 2. Let n(c) = 6*c**5 + 13*c**4 + 4*c**3 + 50*c**2 - 29*c - 11. Let o(p) = -11*b(p) - 2*n(p). Factor o(l).
-l*(l - 1)**2*(l + 2)*(l + 4)
Let q(z) = -5*z**3 + 108*z**2 + 251*z - 106. Let p(h) = h**3 - 21*h**2 - 49*h + 21. Let w(t) = -31*p(t) - 6*q(t). Find y such that w(y) = 0.
-3, 1, 5
Let k = -18350 + 18353. Let n(u) be the second derivative of 19/8*u**4 + 21/8*u**5 + 0 - 32*u - 3*u**2 - 9/7*u**7 - 6/5*u**6 - 2*u**k. Let n(o) = 0. What is o?
-1, -1/2, 2/3
Let d = 242021 + -242018. Solve 2/3*s**d + 48*s - 72 - 10*s**2 = 0.
3, 6
Let n = -3086 + 3088. Let q(i) be the first derivative of 0*i + 10 - 3*i**5 + 405/8*i**n + 5/24*i**6 + 135/8*i**4 - 45*i**3. Factor q(u).
5*u*(u - 3)**4/4
Suppose 5*d = -4*v + v + 37, 4*d - 41 = -3*v. Suppose v*z - 20*z = -9. Find u such that u**4 + 0*u**3 - 2*u + z*u - 3*u**3 - 5*u - u**2 + u**5 = 0.
-2, -1, 0, 1
Let s(g) = 5*g**4 + 3*g**3 - 5*g**2 - 3*g + 2. Let o(v) = 17*v**4 + 11*v**3 - 17*v**2 - 11*v + 7. Let b(u) = -2*o(u) + 7*s(u). Factor b(w).
w*(w - 1)**2*(w + 1)
Let t(f) = f**3 - 29*f**2 + 20*f - 88. Let q(g) = 6*g**3 - 175*g**2 + 73*g - 528. Let m(h) = -2*q(h) + 13*t(h). Factor m(i).
(i - 22)*(i - 4)*(i - 1)
Let s be (-235)/(-80) + (-13)/(-208). Let v(a) be the second derivative of 0*a**2 - 1/8*a**s + 1/80*a**5 - 1/24*a**4 - 6*a + 0. Suppose v(p) = 0. Calculate p.
-1, 0, 3
Let f = -11690 + 11693. Let z(j) be the first derivative of -10/3*j**f - 15/4*j**4 + 0*j**2 - 18 + 0*j - j**5. Let z(t) = 0. What is t?
-2, -1, 0
Let j be 950/(-75)*(0 - 9) + -4. Let n be 280/j - 6/11. Factor 1/2*p**3 + p - 3/2*p**n + 0.
p*(p - 2)*(p - 1)/2
Suppose 212*v = 225*v + 195. Let u be (-2)/5*1 - 30/v. Factor -4/5*a**3 + 12/5*a**5 + 0 + 0*a + 0*a**2 - u*a**4.
4*a**3*(a - 1)*(3*a + 1)/5
Suppose 3*m - 6*m + k = -7, 0 = -3*m - 3*k + 15. Let 60 + 47*o**2 + 2*o**3 + 0*o**3 + 91*o - 15 - o**m = 0. Calculate o.
-45, -1
Let n(q) = -1. Let p(i) = -i**2 - 32*i + 33. Let y be p(-29). Let o = -121 + y. Let b(m) = -2*m**2 - 6*m + 6. Let w(z) = o*b(z) - 10*n(z). Factor w(s).
2*(s + 1)*(s + 2)
Suppose 2*i - 3*w = -i - 195, i + 3*w + 85 = 0. Let g = i - -72. Solve 1/2 - 3/4*j**3 - 7/4*j + g*j**2 = 0.
2/3, 1
Let u(t) = 7. Let c(h) = 3*h**2 - 51*h - 372. Let p(w) = c(w) + 6*u(w). Factor p(o).
3*(o - 22)*(o + 5)
Let v = 2/17959 - -107740/125713. Find i such that 12/7 - v*i**3 - 3/7*i**4 + 24/7*i + 9/7*i**2 = 0.
-2, -1, 2
Let t(c) be the third derivative of c**8/112 + 26*c**7/105 - 163*c**6/120 - 4*c**5/5 + 61*c**4/6 + 40*c**3/3 + 2250*c**2. Solve t(u) = 0 for u.
-20, -1, -1/3, 2
Let q(s) be the third derivative of 5*s**8/336 + 11*s**7/21 - 37*s**6/12 + 7*s**5/3 + 365*s**4/24 - 125*s**3/3 - s**2 - 1207. Suppose q(o) = 0. What is o?
-25, -1, 1, 2
Let a(t) be the first derivative of t**7/140 + t**6/40 - t**4/8 - t**3/3 - 54*t + 57. Let p(c) be the third derivative of a(c). What is m in p(m) = 0?
-1, 1/2
Let l(i) = -14*i + 158. Let o be l(11). Determine c, given that -o + 4*c**2 + 37*c**3 - 66*c - 16 - 31*c**3 - 20*c**2 = 0.
-2, -1/3, 5
Suppose -63/2*f**2 + 29/2*f + 13/2*f**4 + 3 + 15/2*f**3 = 0. What is f?
-3, -2/13, 1
Suppose 853 = 14*f - 883. Suppose f - 124 = -a. Let 2/11*l**3 + a + 2/11*l**2 - 2/11*l**4 - 2/11*l = 0. Calculate l.
-1, 0, 1
Find w, given that -42508549/2*w**3 - 1096209*w**2 - 108 - 18846*w = 0.
-6/349
Find i, given that 198*i**4 - 165*i**2 + 7*i**5 - 188310*i - 1078*i**3 + 190605*i + 594 + 597*i**2 = 0.
-33, -1, -2/7, 3
Let w(z) be the third derivative of -z**8/112 - z**7 - 17*z**6/10 + 7*z**5/2 + 69*z**4/8 + 3*z**2 + 2*z - 37. Let w(f) = 0. Calculate f.
-69, -1, 0, 1
Let g(a) be the first derivative of -34 + 1/15*a**5 - 7/9*a**3 - 1/4*a**4 + 6*a + 5/2*a**2. Solve g(n) = 0.
-2, -1, 3
Factor 81/2 - 1/2*t**2 - 12*t.
-(t - 3)*(t + 27)/2
Determine u, given that -870/11*u**2 - 93294/11*u - 2/11*u**3 + 287766/11 = 0.
-219, 3
Let z be -3 + 62 + (-3 - 3)/6. Let 109*i - 6*i**2 - z*i - 6*i**2 - 33 + 84*i = 0. Calculate i.
1/4, 11
Let 725/6*s**2 + 913/3*s - 1/2*s**4 - 148/3*s**3 + 404/3 = 0. What is s?
-101, -1, -2/3, 4
Factor 0*v - 5/6*v**5 + 0 - 430*v**3 + 1200*v**2 + 130/3*v**4.
-5*v**2*(v - 40)*(v - 6)**2/6
Let r be (-65268)/(-1110)*(-15)/(-27). Factor r - 28*o + 6*o**2.
2*(3*o - 7)**2/3
Let m be 3*4/24*63/42. Let v(l) be the first derivative of 3/2*l**2 + 0*l + 0*l**3 - m*l**4 - 25. Factor v(j).
-3*j*(j - 1)*(j + 1)
Let d(u) be the first derivative of -3015*u**4/4 + 1397*u**3 - 582*u**2 - 12*u - 2033. Suppose d(q) = 0. Calculate q.
-2/201, 2/5, 1
Let p(h) be the first derivative of -h**6/2 + 33*h**5/5 + 9*h**4/4 - 31*h**3 - 33*h**2 + 2989. Suppose p(b) = 0. What is b?
-1, 0, 2, 11
Factor -35*p**2 + 11*p**3 - 188*p**2 + 32*p**2 - 120 - 139*p**2 + 148*p**3 - 36*p**4 + 324*p + 3*p**5.
3*(p - 5)*(p - 2)**3*(p - 1)
Let k(f) = 3*f - 102. Let p be k(34). Let p*m**4 + 140*m - 168 + 11*m**4 + 140*m**2 - 5*m**5 - 145*m**3 + 10*m**5 + 9*m**4 + 8 = 0. Calculate m.
-8, -1, 1, 2
Let l be 6 - ((-60329)/(-2346) - 20 - (-3)/18). Factor 6/17*m**2 - 2/17*m**3 + l - 6/17*m.
-2*(m - 1)**3/17
Let g(f) be the first derivative of 1/6*f**3 - 3/2*f**2 + 5/2*f + 76. Let g(c) = 0. Calculate c.
1, 5
Let b = 162514 - 812556/5. Find o such that 0 + 36/5*o**4 - 4/5*o + 26/5*o**3 - b*o**2 = 0.
-1, -2/9, 0, 1/2
Let -1491/2*d**2 - 26*d**3 + 16807/4 - 1/4*d**4 - 3430*d = 0. What is d?
-49, -7, 1
Let n(y) be the second derivative of y**5/40 - 25*y**4/12 + 28*y**3 - 28*y + 18. Determine t so that n(t) = 0.
0, 8, 42
Suppose 4*v = 5*v, -4 = g + 5*v - 6. Let t(a) be the second derivative of 0*a**3 + 0 - 3/2*a**g - 6*a + 1/4*a**4. Let t(k) = 0. Calculate k.
-1, 1
Let d(v) = 78*v - 53. Let q be d(-6). Let i = -518 - q. Let 0 + 9/2*j**i + 3/2*j**4 + 9/2*j**2 + 3/2*j = 0. What is j?
-1, 0
Let w = 3387 - 3384. Let g(l) be the first derivative of -15 + 0*l**2 + 12*l + 3/4*l**4 - w*l**3. Factor g(d).
3*(d - 2)**2*(d + 1)
Suppose -p - 82 = -4*j, 6 = j - 4*p - 7. Suppose -5*c = -12*c + j. Factor -4*w**4 + w**4 + 0*w**3 - c*w**3.
-3*w**3*(w + 1)
Let h(n) = -3*n**2 - 222*n + 586. Let a(o) = 16*o**2 + 1076*o - 2931. Let u(j) = -6*a(j) - 33*h(j). Factor u(w).
3*(w - 2)*(w + 292)
Let g(m) be the third derivative of -m**8/1344 - 13*m**7/420 - 2*m**6/5 - 6*m**5/5 - 50*m**2 - 8*m. Factor g(t).
-t**