 u(y) be the second derivative of y**7/560 - 11*y**6/480 + 3*y**5/40 - 2*y**4/3 - 6*y. Let l(d) be the third derivative of u(d). Factor l(n).
3*(n - 3)*(3*n - 2)/2
Let q(w) be the first derivative of w**8/8400 - w**6/600 - w**5/300 - 17*w**3/3 + 9. Let r(d) be the third derivative of q(d). Suppose r(o) = 0. Calculate o.
-1, 0, 2
Let d = -29 - -15. Let s be (-3)/((-9)/d) + 5. Factor -2/3*g + 2/3*g**3 + 0 + s*g**4 - 1/3*g**2.
g*(g - 1)*(g + 1)*(g + 2)/3
Factor -75 + 392*l**2 + 100*l**3 - 225 - 807*l**2 + 620*l - 5*l**4.
-5*(l - 15)*(l - 2)**2*(l - 1)
Let i(s) be the second derivative of 5*s**7/42 + 7*s**6/6 + 5*s**5/2 - 5*s**4/6 - 55*s**3/6 - 25*s**2/2 - s + 67. Solve i(u) = 0.
-5, -1, 1
Let i = 118 - 110. Let l be (-45)/126*i + (-8)/(-2). Factor -l*v + 0 - 6*v**3 - 18/7*v**4 - 32/7*v**2.
-2*v*(v + 1)*(3*v + 2)**2/7
Suppose 3/2*p**3 + 0 - 87*p**2 + 0*p = 0. What is p?
0, 58
Let a(d) = d**2 - 6*d + 2. Let g be a(8). Solve g*x**3 - 1111*x**4 - 42*x**2 - 4*x**5 + x**5 - 9 + 33*x + 1114*x**4 = 0 for x.
-3, 1
Let y(a) = 33*a**2 - 66*a + 6. Let w = 63 + -62. Let m(r) = -r**2 + r + 1. Let f(n) = w*y(n) + 6*m(n). Factor f(l).
3*(l - 2)*(9*l - 2)
Let -a**3 - 15*a**2 + 0*a**2 + 57 - 17 + 30*a - 4*a**3 = 0. Calculate a.
-4, -1, 2
Let w(b) = -b + 1. Let p(m) = m**3 + 3*m**2 + 7*m. Let c(s) = s**2 + s - 1. Let t(k) = c(k) + p(k). Let h(o) = t(o) + 3*w(o). Suppose h(z) = 0. What is z?
-2, -1
Let w(a) = -3*a**2 + 9*a. Let n(h) = h**2 - 2*h. Suppose 3*s + 13 = l, l - 4 = -s + 3*l. Let j(z) = s*n(z) - w(z). Find v such that j(v) = 0.
0, 1
Let a(k) be the third derivative of -k**6/480 - 7*k**5/240 - 5*k**4/32 - 3*k**3/8 - 12*k**2 + 2. Factor a(r).
-(r + 1)*(r + 3)**2/4
Let l(u) be the first derivative of 3*u**4/4 - 2*u**3 - 6*u**2 + 24*u - 84. Factor l(p).
3*(p - 2)**2*(p + 2)
Let b = -80 + 150. Let a = b - 1324/19. Factor a*l**3 + 4/19*l**2 - 6/19*l - 4/19.
2*(l - 1)*(l + 1)*(3*l + 2)/19
Let j(o) be the second derivative of -o**6/720 + o**5/120 - o**4/48 + o**3/36 + 7*o**2 - 19*o. Let p(u) be the first derivative of j(u). Factor p(x).
-(x - 1)**3/6
Let y(f) be the third derivative of f**7/420 + f**6/120 - f**5/120 - f**4/24 + 2*f**2 - 13. Factor y(m).
m*(m - 1)*(m + 1)*(m + 2)/2
Let p(b) be the first derivative of -2*b**3/39 - 25*b**2/13 - 48*b/13 + 415. Find d such that p(d) = 0.
-24, -1
Suppose -4*d - 4*l = 156, -11*d + 15*d - 2*l = -138. Let r be 1*-4*d/180. Factor -r*f**3 + 0*f**2 - 2/5*f**4 + 4/5*f + 2/5.
-2*(f - 1)*(f + 1)**3/5
Let c = 28014 + -84041/3. Factor 29/3*r + 10/3 + 7/3*r**3 - c*r**4 + 9*r**2.
-(r - 10)*(r + 1)**3/3
Factor 12*v**3 + 3*v**3 - 66*v**2 + 8*v**3 - 2*v**4 + 62*v - 20 + 3*v**3.
-2*(v - 10)*(v - 1)**3
Let q be ((-2)/7)/(2/(-28)). Factor -7*z**4 - 4*z**2 + 10*z**q + 8*z**2 + 18*z**3 + 11*z**4.
2*z**2*(z + 1)*(7*z + 2)
Let o(g) be the second derivative of 1/66*g**4 - 1/110*g**5 - 1/11*g**2 + 1/33*g**3 + 0 + 23*g. Solve o(j) = 0 for j.
-1, 1
Let c = 89490/17 - 5264. Factor 12/17*j**3 - 2/17*j**4 - c*j**2 - 48/17*j - 32/17.
-2*(j - 4)**2*(j + 1)**2/17
Let t(c) be the second derivative of -c**5/90 + 4*c**4/27 - 17*c**3/27 + 10*c**2/9 - 3*c - 21. Factor t(v).
-2*(v - 5)*(v - 2)*(v - 1)/9
Let k(m) = -4*m + 6. Let q be k(-3). Suppose 4*a - 6 - 14 = -3*i, a - q = -4*i. Determine s, given that -4*s**4 + 3*s**3 + 4*s**a - s**4 + 3*s**4 - 5*s**3 = 0.
-2, 0, 1
Let y(a) be the second derivative of -5*a**4/12 + 650*a**3/3 - 42250*a**2 + 317*a. Suppose y(t) = 0. Calculate t.
130
Let r(h) = h**3 - 7*h**2 + 9*h - 1. Let b be r(5). Let v be (-7 - b)*(-2 - (-10)/7). Factor 2/7*w**3 + 0 + v*w + 6/7*w**2.
2*w*(w + 1)*(w + 2)/7
Let f(x) be the third derivative of -2*x**7/315 + 7*x**6/90 - 2*x**5/5 + 10*x**4/9 - 16*x**3/9 + 2*x**2 + 43*x. Find j, given that f(j) = 0.
1, 2
Let g(f) = -f - 8. Let p be g(-11). Suppose p*t - 4*t = -16. Solve 72*y**2 - 17*y**3 - 8*y**2 + 45*y**3 + t*y = 0.
-2, -2/7, 0
Let u = 1165 + -1163. Factor 1/3*i + 2/3*i**u - 1/3*i**3 - 2/3.
-(i - 2)*(i - 1)*(i + 1)/3
Let u be (-222)/(-2016) + ((-27)/(-21) - 1). Let y = u - -15/16. Factor -2*x + y + 2/3*x**2.
2*(x - 2)*(x - 1)/3
Let x = 335 + -333. Let z(p) be the first derivative of 1/10*p**5 - 1/24*p**6 - 1 - 1/16*p**4 + 0*p**3 + 0*p**x + 0*p. Factor z(t).
-t**3*(t - 1)**2/4
Let a(s) be the first derivative of -s**4/36 + 2*s**3/27 + s**2/18 - 2*s/9 + 83. Factor a(x).
-(x - 2)*(x - 1)*(x + 1)/9
Let w(g) = -29*g**2 + 540*g + 11. Let c(t) = -5*t**2 + 108*t + 2. Let v(o) = -11*c(o) + 2*w(o). Factor v(z).
-3*z*(z + 36)
Let p(r) = -4. Let g(x) = 1. Let i(t) = 15*g(t) + 5*p(t). Let n(d) = d**2 + d + 13. Let l(u) = 15*i(u) + 5*n(u). Find a such that l(a) = 0.
-2, 1
Let u(t) be the third derivative of 1/4*t**3 - 10*t**2 + 1/240*t**6 - 1/48*t**4 + 0 - 1/40*t**5 + 0*t. Factor u(g).
(g - 3)*(g - 1)*(g + 1)/2
Let r(z) be the third derivative of z**7/245 + z**6/105 - 13*z**5/210 + z**4/14 + 2*z**2 - 32*z. Suppose r(v) = 0. What is v?
-3, 0, 2/3, 1
Let c(h) be the first derivative of h**4/20 - 2*h**3/15 + h**2/10 - 450. Determine j, given that c(j) = 0.
0, 1
Let m(a) be the second derivative of -9*a**5/50 + 7*a**4/30 + 2*a**3/15 - 91*a. Factor m(h).
-2*h*(h - 1)*(9*h + 2)/5
Let t(h) be the first derivative of h**3/9 + 112*h**2/3 + 12544*h/3 + 743. Determine j, given that t(j) = 0.
-112
Let n(v) be the first derivative of -v**7/840 - v**6/160 - v**5/80 - v**4/96 - 7*v**2 - 10. Let t(w) be the second derivative of n(w). Factor t(l).
-l*(l + 1)**3/4
Let u(o) be the third derivative of 1/140*o**6 - 1/210*o**5 + 0*o**3 - 1/245*o**7 + 0*o + 2*o**2 + 1/1176*o**8 + 0*o**4 + 0. Factor u(f).
2*f**2*(f - 1)**3/7
Suppose 2*x - 2*h + 2 = 0, 19 = 6*x - x + 3*h. Let f(y) be the second derivative of 9*y - 1/7*y**3 - 1/42*y**4 - 2/7*y**x + 0. Determine o, given that f(o) = 0.
-2, -1
Let d be (1*2 + 0/10)/1. Let u(v) be the first derivative of 2/35*v**5 + 0*v**d - 1/21*v**6 + 0*v**3 + 0*v + 0*v**4 - 3. Factor u(t).
-2*t**4*(t - 1)/7
Let v be (-4)/2 + 45/((-12555)/(-806)). Factor 2/9*s**4 + 4/9*s**3 - 16/9*s - 2/3*s**2 - v.
2*(s - 2)*(s + 1)**2*(s + 2)/9
Suppose 0 = 4*d - 79 + 31. What is y in -3*y + d*y**4 + 3*y**4 + 7*y**2 + 23*y**3 + 4*y + 2*y**2 = 0?
-1, -1/3, -1/5, 0
Let t(g) be the third derivative of -9*g**2 + 0 - 1/15*g**5 + 0*g + 2/3*g**4 + 1/360*g**6 - 32/9*g**3. Solve t(o) = 0 for o.
4
Let w(u) be the first derivative of -5*u**3/3 - 20*u**2 - 35*u + 6. What is p in w(p) = 0?
-7, -1
Let d(c) be the first derivative of 1/20*c**4 + 0*c + 1/10*c**2 + 4 - 2/15*c**3. Find t, given that d(t) = 0.
0, 1
Let f be ((-1350)/(-20250))/((-1 + -1)/(-108)). Factor -f*b + 2/5*b**2 + 28/5.
2*(b - 7)*(b - 2)/5
Suppose 0 = 7*a + 4 - 18. Let t(b) be the second derivative of -3*b + 6*b**a - 2*b**3 + 0 + 1/4*b**4. Find m, given that t(m) = 0.
2
Suppose 8*m + 28 = 44. Suppose -4*z - 5 = z, m*r - 3*z = 7. Determine w so that 1/3*w**3 - 2/3 + 0*w**r - w = 0.
-1, 2
Determine w so that -1/6*w**2 - 40/3 - 1/12*w**3 + 16/3*w = 0.
-10, 4
Factor -338/5 - 2/5*s**2 - 52/5*s.
-2*(s + 13)**2/5
Let r(w) be the second derivative of w**4/6 + 74*w**3/3 + 1369*w**2 + 51*w. Suppose r(u) = 0. Calculate u.
-37
Determine t so that 1/4*t**2 - 9/2*t + 0 = 0.
0, 18
Let p(g) = -46*g + 18 - 11*g**2 - 26 - 6*g + 34*g**2. Let d(c) = -24*c**2 + 51*c + 9. Let n(w) = 4*d(w) + 3*p(w). Factor n(m).
-3*(m - 2)*(9*m + 2)
Suppose 3*s - 5 = 4*s. Let c be (-126)/(-84)*(1 - s/3). Factor 5/2*y**c + 1/2 + 1/2*y**5 + 5/2*y + 5*y**3 + 5*y**2.
(y + 1)**5/2
Let y(u) be the first derivative of u**6/15 + 2*u**5/5 + u**4/2 - 2*u**3/3 - 6*u**2/5 - 109. Find o such that y(o) = 0.
-3, -2, -1, 0, 1
Let s be (-2)/10 - 82/(-435). Let r = s + 119/261. Factor -2/9*u + 0 + r*u**3 + 2/9*u**2.
2*u*(u + 1)*(2*u - 1)/9
Let d(c) be the second derivative of -1/150*c**6 + 10*c + 0*c**4 + 0 - 1/50*c**5 + 1/15*c**3 + 1/10*c**2. Find u, given that d(u) = 0.
-1, 1
Let y(n) be the second derivative of n**7/168 - n**5/20 - 2*n + 6. Factor y(q).
q**3*(q - 2)*(q + 2)/4
Let i(u) = 5*u. Let o be i(5). Suppose o = 3*j + 2*j. Solve -22*c**2 + 15*c**3 - j*c**3 + 8*c**3 + 4*c = 0.
0, 2/9, 1
Factor 13/6*r - 1/3*r**2 + 4.
-(r - 8)*(2*r + 3)/6
Let z(d) be the second derivative of -d**7/5880 - d**6/336 - 3*d**5/140 + 7*d**4/6 + 10*d. Let y(r) be the third derivative of z(r). Factor y(v).
-3*(v + 2)*(v + 3)/7
Let