*6/120 + h**5/60 - 5*h**3/6 - 11*h**2. Let o(f) be the first derivative of x(f). Solve o(n) = 0 for n.
-2, 0, 1
Let x(p) = 11*p**4 - 22*p**3 + 7*p**2 + 4*p. Let u(z) = -43*z**4 + 87*z**3 - 27*z**2 - 17*z. Let a(f) = 4*u(f) + 18*x(f). Factor a(o).
2*o*(o - 1)**2*(13*o + 2)
Suppose -5*j + 4*d + 24 = 6*d, 0 = -5*d - 15. Solve -u - 2862*u**2 + 7*u - 22*u**3 - 12 + 16*u + 2868*u**2 + j*u**4 = 0.
-1, 2/3, 1, 3
Let a(f) = -f - 1. Let h be a(-4). Determine v, given that 3*v**h - 4*v**2 - 4 - 20*v - 8 + v**3 = 0.
-1, 3
Let 0 - 15/4*s**4 - 33/4*s**2 + 9/4*s + 39/4*s**3 = 0. What is s?
0, 3/5, 1
Let g be (-8)/(-44) - 106/(-22). Suppose 0 = p + 1, t = -7*p + g*p. Let -1/5*k**4 + 0 + 1/5*k**3 + 0*k + 0*k**t = 0. Calculate k.
0, 1
Let g(p) be the second derivative of -p**9/105840 - p**8/15680 - p**7/8820 - 5*p**4/12 - 8*p. Let z(w) be the third derivative of g(w). Factor z(k).
-k**2*(k + 1)*(k + 2)/7
Suppose 3*i = 0, i - 52 = 4*h - 3*i. Let z be 11 + h + 16/7. Let -12/7*t - 18/7 - z*t**2 = 0. What is t?
-3
Factor 1/6*t**2 - 8/3 + 0*t.
(t - 4)*(t + 4)/6
Suppose -r = 4*r - 5. Suppose i - 3*o - r - 2 = 0, i + 4*o - 3 = 0. Find z, given that -7*z**3 + z**2 - 3*z**4 - i*z**2 + 3*z**3 + z**4 = 0.
-1, 0
Let f(u) be the first derivative of -u**3/6 - 7*u**2/12 + u - 68. Factor f(y).
-(y + 3)*(3*y - 2)/6
Let m(l) be the first derivative of 0*l + 1/180*l**6 + 4/3*l**3 + 1/6*l**4 + 0*l**2 + 1/20*l**5 - 5. Let d(j) be the third derivative of m(j). Factor d(x).
2*(x + 1)*(x + 2)
Let r(q) be the third derivative of -q**8/3024 + q**7/1890 + q**6/135 - q**5/45 - 185*q**2 - 2*q. Let r(z) = 0. Calculate z.
-3, 0, 2
Let a = 57 - 60. Let w = 7 - 12. Let g(r) = -6*r**4 - r**3 + 12*r**2 + 5. Let y(l) = 3*l**4 - 6*l**2 - 3. Let n(s) = a*g(s) + w*y(s). Factor n(f).
3*f**2*(f - 1)*(f + 2)
Let w(z) be the third derivative of 13/90*z**5 - 1/18*z**4 + 0 + 0*z - 8/9*z**3 - 34*z**2 - 1/60*z**6. Find q, given that w(q) = 0.
-2/3, 1, 4
Let 2*r**2 - 45*r - 21*r - 52 + 16*r = 0. What is r?
-1, 26
Suppose -29*x = 68*x - 194. Let k(m) be the third derivative of 1/420*m**7 + 0*m**5 + 0 + 0*m - 1/120*m**6 - 1/12*m**3 + 11*m**x + 1/24*m**4. Factor k(l).
(l - 1)**3*(l + 1)/2
Let c(t) be the first derivative of -5*t**6/12 + 3*t**5/4 - 5*t**3/12 - 11. Determine p, given that c(p) = 0.
-1/2, 0, 1
Let 1007 + 10*r**3 - 1997 + 65*r + 105*r**2 + 1000 - 40*r**4 = 0. What is r?
-1, -1/2, -1/4, 2
Let t be ((-96)/9)/(-2)*125/1000. Factor 1 - t*a - 1/3*a**2.
-(a - 1)*(a + 3)/3
Let d(m) = m + 5. Let c be d(5). Let q be (18/15)/(4/c). Suppose 2/11*a**2 + 6/11*a - 6/11*a**q - 4/11 + 2/11*a**4 = 0. Calculate a.
-1, 1, 2
Suppose 2*q = 5*q - 12*q. Suppose -3*l + 12 = q, -5*l + 12 = -4*w - 0*l. Let -2/3*i**2 - 4/3 - w*i = 0. What is i?
-2, -1
Let a = -52 - -55. Suppose 0*j + j - 138*j**a + 137*j**3 = 0. What is j?
-1, 0, 1
Let s(q) be the third derivative of 0*q + 31/735*q**7 + 0 - 5/294*q**8 - 1/30*q**5 + 0*q**3 - 1/84*q**4 + 13*q**2 - 1/140*q**6. Let s(d) = 0. Calculate d.
-1/4, -1/5, 0, 1
Let g(o) = 39*o**2 + 117*o - 116. Let p(c) = -32*c**2 - 116*c + 116. Let l(y) = 4*g(y) + 5*p(y). Factor l(x).
-4*(x - 1)*(x + 29)
Let t(q) = q**2. Let m be t(-6). Suppose 3 + 16*c - 3 - m*c + 4*c**2 = 0. What is c?
0, 5
Let o = -8 + 22. Suppose x - o = -5*h, x - 2*x = h - 6. Find u such that -19*u + x*u**2 + 19*u - 4*u**3 = 0.
0, 1
Let a(o) = -o**2 - 18*o + 7. Let h be a(-17). What is f in -4*f**4 + 20*f + 45 - h*f**3 + 45*f**2 - 9 - 77*f**2 + 4*f = 0?
-3, -1, 1
Let s be 569220/2380 - 4/(-34). Let w = -239 + s. Factor 8/7 - w*p**2 + 0*p.
-2*(p - 2)*(p + 2)/7
Suppose -t + 3 = 2. Let v(l) = 6 + 0*l**2 + 0*l**2 - 9*l - 2*l**2 - t. Let c(h) = h**2 + 4*h - 2. Let m(i) = 5*c(i) + 2*v(i). Let m(d) = 0. Calculate d.
-2, 0
Determine o so that 169/2*o**3 + 184*o - 9/2*o**5 + 30 + 479/2*o**2 - 11/2*o**4 = 0.
-3, -2, -1, -2/9, 5
Let n(q) be the first derivative of -24/35*q**5 - 4/7*q**3 - 7 + 1/7*q**2 + 0*q + 13/14*q**4 + 4/21*q**6. Suppose n(z) = 0. Calculate z.
0, 1/2, 1
Determine r so that -16*r - 17*r**3 - 10*r**3 + 39*r**3 - 16*r**3 + 20*r**2 = 0.
0, 1, 4
Let r(y) be the third derivative of -5*y**8/336 + 2*y**7/21 + 43*y**6/8 + 131*y**5/3 + 190*y**4/3 - 800*y**3 - 17*y**2 + 6*y. Suppose r(n) = 0. What is n?
-4, 1, 15
Let i = 22 - 22. Find o such that -9*o + 8*o + i*o**2 - 3*o + 2*o**2 = 0.
0, 2
Factor -2/3*y**2 - 14/3*y - 20/3.
-2*(y + 2)*(y + 5)/3
Let g(y) = 21*y**3 + 249*y**2 + 324*y + 90. Let z(p) = 23*p**3 + 250*p**2 + 325*p + 90. Let a(v) = 4*g(v) - 3*z(v). Determine d so that a(d) = 0.
-15, -1, -2/5
Let h(s) be the second derivative of -4*s + 4/3*s**3 + 1/2*s**4 + 0 + s**2. Let h(x) = 0. Calculate x.
-1, -1/3
Let w(d) be the first derivative of -3/5*d**4 + 8/15*d**3 - 1/5*d**2 + 55 - 1/15*d**6 + 8/25*d**5 + 0*d. Solve w(b) = 0 for b.
0, 1
Suppose 20 = m - 4*k, 0 = -5*m + 2*k - 3*k - 5. Let u(g) be the first derivative of 10 + 1/36*g**4 + 4/27*g**3 + 2/9*g**2 + m*g. Solve u(h) = 0.
-2, 0
Let s(c) be the first derivative of -2*c**5/5 - 9*c**4/2 - 58*c**3/3 - 39*c**2 - 36*c + 274. Factor s(q).
-2*(q + 1)*(q + 2)*(q + 3)**2
Let t(o) be the second derivative of -o**5/690 - o**4/92 - 2*o**3/69 - 8*o**2 - o. Let z(n) be the first derivative of t(n). Factor z(k).
-2*(k + 1)*(k + 2)/23
Suppose -552 + 122 = -109*i + 6. Solve 0*v - 4/3*v**2 + 2/3*v**3 + 4/3*v**i + 0 - 2/3*v**5 = 0 for v.
-1, 0, 1, 2
Let x be ((-60)/62 + 1)/(59/649). Let z = 241/155 - x. Find c, given that -z*c**2 - 14/5*c - 4/5 = 0.
-2, -1/3
Let u(b) be the second derivative of 25*b**7/21 - 23*b**6/6 + 13*b**5/20 + 10*b**4/3 - 2*b**3 + b + 22. Let u(y) = 0. What is y?
-3/5, 0, 2/5, 1/2, 2
Let b be (-9)/(-15)*(-10)/(-2). Let k(o) = -9*o + 31. Let v be k(b). Find c, given that 2/5*c**3 - 2/5*c - 1/5*c**v + 0*c**2 + 1/5 = 0.
-1, 1
Let r = -580 + 580. Let m(n) be the second derivative of 1/114*n**4 + 0 + 0*n**3 - 1/190*n**5 + r*n**2 - 4*n. Let m(k) = 0. Calculate k.
0, 1
Let q = 1263/4 + -312. Find z such that 3/4*z**3 - 3/4*z**2 - q*z - 9/4 = 0.
-1, 3
Let w(z) be the third derivative of -5*z**8/336 - 2*z**7/21 - z**6/8 - 57*z**2. Solve w(j) = 0 for j.
-3, -1, 0
Let x(d) = -d**3 + 3*d**2 - 20*d - 21. Let u be x(-1). Factor 2/3*z**4 + 2/3*z - 2*z**2 - 2/3*z**u + 4/3.
2*(z - 2)*(z - 1)*(z + 1)**2/3
Let w(h) be the first derivative of 2*h**5/25 + h**4/10 - 2*h**3/5 - h**2/5 + 4*h/5 + 52. Suppose w(z) = 0. Calculate z.
-2, -1, 1
Let r = -1354 + 1957. Factor -4*i - 605*i**2 + 12*i - 8 + r*i**2.
-2*(i - 2)**2
Suppose 0 = l, -5*l - 3 - 2 = -o. Suppose -5*a + 4*a + 2 = 0. Find z, given that -180*z - 152*z**4 + 59*z**o + 530*z**4 + 88*z**5 - 24 - 354*z**a + 33*z**3 = 0.
-2, -1, -2/7, 1
Let s be (-19 - -21)/((-12)/31). Let k = -143/30 - s. Solve k*t**2 + 8/5 - 8/5*t = 0.
2
Let d(t) be the third derivative of t**6/420 - 9*t**5/70 + 65*t**4/28 - 169*t**3/21 - 207*t**2. Determine a so that d(a) = 0.
1, 13
Let j = -25558/15 - -1704. Factor 0*l + 2/15*l**4 + 0*l**3 + 0 - j*l**2.
2*l**2*(l - 1)*(l + 1)/15
Let u(w) be the third derivative of -w**6/96 + w**5/40 - w**4/96 - 99*w**2 + 1. Factor u(l).
-l*(l - 1)*(5*l - 1)/4
Let r = -136 + 410/3. Determine k so that 2/15*k**2 + r*k + 8/15 = 0.
-4, -1
Factor -13/8*g - 3/2 + 13/8*g**3 + 1/8*g**4 + 11/8*g**2.
(g - 1)*(g + 1)**2*(g + 12)/8
Let n(h) = -h**4 + 4*h**2 + 3*h. Let z(y) = y**3 + y**2. Let c(o) = 3*n(o) + 3*z(o). Factor c(i).
-3*i*(i - 3)*(i + 1)**2
Suppose 0*f + 7*f = 21, 4*f = 2*g + 8. Let 0 + 2/3*x**5 + 128/3*x - 12*x**4 + 194/3*x**3 - 96*x**g = 0. What is x?
0, 1, 8
Let t(l) be the second derivative of -l**7/84 - l**6/30 + l**4/12 + l**3/12 - 63*l. Determine d so that t(d) = 0.
-1, 0, 1
Let n(h) be the third derivative of 1/504*h**8 + 2/315*h**7 + 0 + 0*h**4 + 1/180*h**6 + 0*h + 9*h**2 + 0*h**3 + 0*h**5. Factor n(l).
2*l**3*(l + 1)**2/3
Let s(f) = f - 5. Let v be s(8). Find a such that 10*a**3 - 13*a**v - 10 + 9*a**2 - 2 = 0.
-1, 2
Let w(q) be the first derivative of -16/3*q**3 + 4 - 1/30*q**5 - 2/3*q**4 + 3*q**2 + 0*q. Let j(n) be the second derivative of w(n). Factor j(r).
-2*(r + 4)**2
Let o be 3*346/1428 - (-1)/(-2). Let a = o + 1/17. Factor a - 2/7*w**2 + 0*w.
-2*(w - 1)*(w + 1)/7
Let b(q) = q**3 + 5*q**2 - q - 1. Let z be b(-5). Factor 3*w**3 + 0*w**3 - 8*w**3 - w + z*w**3 + 2*w**2.
-w*(w - 1)**2
Let k(l) be the second derivativ