)**2*(3*j + 1)/7
Let l(y) be the third derivative of y**8/1344 + y**7/105 + y**6/20 + 17*y**5/120 + 23*y**4/96 + y**3/4 - 68*y**2. Find b such that l(b) = 0.
-3, -2, -1
Suppose 0 = 14*b - 171 + 59. Let w = 0 - -2. Let -14 + 25*v**2 - b*v - 21*v**2 + w = 0. What is v?
-1, 3
Let i(g) = 3*g**4 + 194*g**3 + 3070*g**2 - 2. Let a(o) = 12*o**4 + 777*o**3 + 12279*o**2 - 9. Let p(b) = 2*a(b) - 9*i(b). Find c such that p(c) = 0.
-32, 0
Suppose 5*w - 16 = -7*t + 8*t, 2*w = -5*t - 26. What is f in 2/3*f**w + 0 + 0*f = 0?
0
Let v(r) be the first derivative of r**3/3 - 19*r**2/2 - 20*r - 4. Solve v(t) = 0.
-1, 20
Let k(p) be the third derivative of -p**6/280 - 4*p**5/35 - 29*p**4/56 - p**3 - 507*p**2. Factor k(b).
-3*(b + 1)**2*(b + 14)/7
Let y(j) be the second derivative of j**8/2352 + j**7/735 - j**6/840 - j**5/210 - 12*j**2 - 22*j. Let t(o) be the first derivative of y(o). Factor t(n).
n**2*(n - 1)*(n + 1)*(n + 2)/7
Suppose 0 = 3*j + 5*g + 14, 5*j - 3*g - 85 = -63. Let 50/11 + 20/11*u + 2/11*u**j = 0. Calculate u.
-5
Let x(b) = b**2 - b - 2. Let y(q) = 230*q + 6502. Let p(v) = 2*x(v) + y(v). Factor p(o).
2*(o + 57)**2
Let o be (-2117)/116 - (1 - (-10)/(-8)). Let q be 3/o*-4*81/18. Factor -2/17*r + 0 - 4/17*r**4 - 8/17*r**2 - 10/17*r**q.
-2*r*(r + 1)**2*(2*r + 1)/17
Let q = -57295/6 + 9550. Factor -1/6*i**3 - 7/6*i + 1/2 + q*i**2.
-(i - 3)*(i - 1)**2/6
Let x(k) be the third derivative of k**6/180 - 7*k**5/450 + k**4/90 + 20*k**2 + k. Find w, given that x(w) = 0.
0, 2/5, 1
Suppose -5 = -y - 2. Let a(r) be the first derivative of 1/3*r**6 + 0*r + 0*r**4 + 2/5*r**5 + 0*r**2 + 0*r**y + 5. Factor a(g).
2*g**4*(g + 1)
Suppose 66*b - 15 = -g + 69*b, -20 = 5*g + 4*b. Determine q so that 2/9*q**2 - 2/9*q + g = 0.
0, 1
Let j(r) be the third derivative of r**8/120 + 58*r**7/525 - 97*r**6/150 + 82*r**5/75 - 13*r**4/60 - 22*r**3/15 - r**2 - 93. Find n such that j(n) = 0.
-11, -2/7, 1
Let c be 438/(-792) - (-1)/4. Let v = 1/33 - c. Factor i**2 + 1/3*i + v*i**4 + i**3 + 0.
i*(i + 1)**3/3
Let v(i) be the second derivative of i**6/150 - 9*i**5/100 + 23*i**4/60 - i**3/10 - 18*i**2/5 + 1086*i. Factor v(o).
(o - 4)*(o - 3)**2*(o + 1)/5
Let o = 17392 + -69547/4. Determine n so that o*n**4 + 6*n - 17/4*n**2 - 1 - 5/4*n**5 - 19/4*n**3 = 0.
-1, 1/5, 1, 2
Let j be (1 - -1)/(4/6). Let i(u) be the first derivative of 1/2*u**2 - 1/2*u**4 + 0*u**j + 4 + 0*u**5 + 1/6*u**6 + 0*u. Factor i(r).
r*(r - 1)**2*(r + 1)**2
Determine g so that -33/4*g**4 + 75/2*g + 0 - 99/4*g**3 - 15/4*g**2 - 3/4*g**5 = 0.
-5, -2, 0, 1
Let z(l) be the second derivative of -l**6/120 - 3*l**5/40 - 13*l**4/48 - l**3/2 - l**2/2 - 62*l. Suppose z(k) = 0. What is k?
-2, -1
Let d(u) be the second derivative of u**5/5 + 119*u**4/12 - 5*u**3 - 49*u - 1. Factor d(i).
i*(i + 30)*(4*i - 1)
Let o(v) be the second derivative of -10*v + 1/6*v**3 + 0 + 1/240*v**5 + 1/24*v**4 + 9/2*v**2. Let k(x) be the first derivative of o(x). Factor k(z).
(z + 2)**2/4
Let q(o) be the first derivative of -4*o**5/45 + o**4/2 - 28*o**3/27 + o**2 - 4*o/9 + 348. Let q(g) = 0. What is g?
1/2, 1, 2
Let p(z) be the third derivative of z**5/75 + 224*z**4/15 + 100352*z**3/15 + 34*z**2 + 7*z. Determine t, given that p(t) = 0.
-224
Let b be (-3)/1 + 45 + 6. Solve g**3 - b*g**5 + 2*g**2 + 2*g**3 - 10*g**4 - g**3 + 54*g**5 = 0 for g.
-1/3, 0, 1
Let o be ((-5)/4)/(10/(-40)) + 270/(-90). Factor 1/2*t**3 + 0 + 0*t + 0*t**o.
t**3/2
Suppose 242 - 9*v**3 - 418*v - 255/2*v**2 = 0. Calculate v.
-22/3, 1/2
Let i(k) be the first derivative of 0*k + 0*k**2 - 3/10*k**5 - 1/2*k**3 - 16 - 3/4*k**4. Factor i(a).
-3*a**2*(a + 1)**2/2
Let q = 1035 - 1035. Let n(c) be the first derivative of q*c**2 + 0*c + 0*c**3 - 1/14*c**4 + 9 + 2/35*c**5. Factor n(l).
2*l**3*(l - 1)/7
Suppose -k = -5*r + 13 + 60, -51 = -3*r - 3*k. Let v be 5*-4*(-3)/r. Determine f so that 0 - 3/5*f**v + 3/5*f**3 + 0*f**2 + 0*f = 0.
0, 1
Let x(q) = -q**3 - 3*q**2 + q + 6. Let l be x(-3). Factor r**l + 21*r**2 - 16*r - 6*r**2 - 9*r + 8*r**3 + r**4.
r*(r - 1)*(r + 5)**2
Solve 36/7 + 16/7*b**2 - 2/7*b**3 - 6*b = 0 for b.
2, 3
Let a(l) be the first derivative of -30 - 2/15*l**3 - 16/5*l + 6/5*l**2. Find y such that a(y) = 0.
2, 4
Let p(n) = -4*n**3 + 5*n**5 + 0*n**5 + 3*n + 4*n**4 - 8*n**2 + 4 + 2*n + 3*n**4. Let o(t) = -t**5 - t**4 - t. Let k(l) = 3*o(l) + p(l). What is c in k(c) = 0?
-2, -1, 1
Let 13/3*c + 10/9 + 4*c**2 = 0. Calculate c.
-2/3, -5/12
Let g(l) be the first derivative of l**4/12 - l**3/6 - l**2 + 6*l + 3. Let w(y) be the first derivative of g(y). Let w(t) = 0. What is t?
-1, 2
Let v be (-6)/5 - (-36)/30. Let d(x) be the first derivative of v*x + 1/3*x**2 - 1/3*x**5 - 2/3*x**4 - 3 - 1/9*x**3. Factor d(t).
-t*(t + 1)**2*(5*t - 2)/3
Factor 78*n - 6*n**4 + 57/2*n**3 - 36 - 67*n**2 + 1/2*n**5.
(n - 3)**2*(n - 2)**3/2
Let f = 82 + -90. Let j(t) = 6*t**5 + 6*t**4 - 9*t**3 - 3*t**2. Let v(h) = 17*h**5 + 17*h**4 - 26*h**3 - 8*h**2. Let p(z) = f*j(z) + 3*v(z). Factor p(s).
3*s**3*(s - 1)*(s + 2)
Let z be 84/30*96/224. Factor -z*y**2 + 0 + 3/5*y.
-3*y*(2*y - 1)/5
Suppose 3*o + 285 = 294. Suppose 0 = -3*r + 1 + 11. Factor 2/5*d**r + 8/5 + 26/5*d**2 - 24/5*d - 12/5*d**o.
2*(d - 2)**2*(d - 1)**2/5
Suppose 189 = 6*n - 381. Let p = n + -95. Determine z, given that 2/13*z**3 + 0 + 0*z - 2/13*z**4 + p*z**2 = 0.
0, 1
Let l(g) = -81*g + 658. Let h be l(8). Let 5/2*o**2 - h*o + 15/2 = 0. Calculate o.
1, 3
Let o(y) = y + 11. Let h be o(-8). Suppose t + t**3 - 5*t**h - 3*t**2 + 6*t**3 = 0. Calculate t.
0, 1/2, 1
Let t = 11 + -15. Let x(n) = 1 + 21*n**2 - 27*n - 42*n - 3 - 4. Let y(p) = 3*p**2 - 10*p - 1. Let d(z) = t*x(z) + 27*y(z). Determine l so that d(l) = 0.
1
Let n(b) = 22*b**3 + 232*b**2 + 445*b + 96. Let v(l) = 32*l**3 + 348*l**2 + 668*l + 144. Let p(r) = 8*n(r) - 5*v(r). Factor p(o).
4*(o + 3)*(o + 4)*(4*o + 1)
Let y(l) = -l**2 + l - 1. Let u(t) = -9*t**2 + 364*t - 31692. Let g(w) = -3*u(w) + 24*y(w). Factor g(m).
3*(m - 178)**2
Factor -10*f**3 - 9*f**3 + 28*f**4 - 2*f**5 - 2*f**3 - 5*f**3.
-2*f**3*(f - 13)*(f - 1)
Suppose -186 - 324 = -255*b. Let 1/2*q**4 - 1/2*q**b + 0 + 1/2*q**3 - 1/2*q = 0. Calculate q.
-1, 0, 1
Let a be (-51)/(-306)*27/9. Let m(l) = l**3 - l**2 - 4*l - 1. Let p be m(3). Let 1/2*s**3 + 0 + a*s**p + 0*s**2 + 0*s - s**4 = 0. What is s?
0, 1
Let h = 9 + -9. Suppose 0 = -h*u - 3*u + 4*s + 22, -3*u + 3*s + 18 = 0. Factor 6*g**u + 0*g**2 - 6*g**3 + 40*g + 20 - g**2 - 9*g**3.
-5*(g - 2)*(g + 1)*(3*g + 2)
Let c(q) be the third derivative of q**10/30240 - q**9/6048 + 2*q**5/15 + 5*q**2. Let b(z) be the third derivative of c(z). Factor b(d).
5*d**3*(d - 2)
Suppose -5*k + 5 = -10*k. Let o = k - -3. Suppose 1/3*g**2 + 3 + o*g = 0. What is g?
-3
Let g = -660 - -3302/5. What is t in 0 - g*t - 2/5*t**2 = 0?
-1, 0
Let -148/19 + 218/19*q - 68/19*q**2 - 2/19*q**3 = 0. Calculate q.
-37, 1, 2
Let u(d) = d**2 + 28*d - 240. Let a be u(-35). Let o(c) be the third derivative of -11*c**2 + 0*c + 0 + 0*c**3 + 1/20*c**a + 1/8*c**4. Factor o(n).
3*n*(n + 1)
Suppose -56 = -4*t + 4*q, 6*t + 3*q - 18 = 5*t. Factor -3*z**2 + t*z**4 - 12*z**4 - 6*z**4 - 6*z**3.
-3*z**2*(z + 1)**2
Let g = -29 + 24. Let b = g - -40. Let t(s) = -85*s**3 - 50*s**2 + 85*s + 85. Let o(j) = 5*j**3 + 3*j**2 - 5*j - 5. Let u(a) = b*o(a) + 2*t(a). Factor u(r).
5*(r - 1)*(r + 1)**2
Suppose 51/4*m + 3/2 + 21/4*m**3 + 33/2*m**2 = 0. What is m?
-2, -1, -1/7
Let p be (21/245)/((-15)/(-200) + (-12)/(-96)). Let l be 25/9 + (-4)/(-18). Solve -9/7*k + p*k**4 + 9/7*k**l + 3/7*k**2 - 6/7 = 0 for k.
-2, -1, 1
Solve -49*z + 4*z**2 - 488 - 240*z - 43*z - 152*z = 0 for z.
-1, 122
Let 0*w**2 + 6*w**2 - 4*w**4 + 8 - 12*w**3 - 6*w**2 + 12*w - 4*w**2 = 0. Calculate w.
-2, -1, 1
Let g(r) = r**2 + 14*r + 13. Suppose 5*v + 15 = -50. Let c be g(v). Determine b, given that 2/11*b**4 + c - 10/11*b**5 + 10/11*b**3 - 2/11*b**2 + 0*b = 0.
-1, 0, 1/5, 1
Let g(a) = a**3 - 14*a**2 - 13*a - 28. Let m be g(15). Factor 6*h**4 + 45*h**5 - 6*h**m + h - 4*h - 42*h**5.
3*h*(h - 1)*(h + 1)**3
Let f(w) = 2*w**4 + w**3 + 7*w**2 - 10*w + 5. Let g(h) = 2*h**4 + 6*h**2 - 8*h + 4. Let v(y) = 4*f(y) - 5*g(y). Factor v(u).
-2*u**2*(u - 1)**2
Let y(t) be the first derivative of 12 + 2*t - 4/7*t**2 + 5/21*t**3 - 1/42*t**4. Let j(w) be the first derivative of y(w). Factor j(n).
-2*(n - 4)