 f(y) be the second derivative of -y**7/6300 + y**6/1350 + y**5/225 - 2*y**4/45 - 7*y**3/3 - 14*y. Let l(r) be the second derivative of f(r). Factor l(t).
-2*(t - 2)**2*(t + 2)/15
Suppose m = -2*p + 8, -21 + 5 = -4*p - 5*m. Find o, given that -10 - 2*o**2 + p*o**5 + 12*o**2 + 15*o - 20*o**3 - 4*o**5 + 5*o**5 = 0.
-2, -1, 1
Let b be 16/56 + (1510/(-385) - -4). Find q, given that 4/11 - 30/11*q**3 + 2*q + b*q**2 = 0.
-2/3, -1/5, 1
Let x(g) be the first derivative of -g**3 - 75*g**2/2 - 72*g + 77. Factor x(t).
-3*(t + 1)*(t + 24)
Determine m, given that -48/7*m**2 + 0 + 330/7*m**4 + 8/7*m - 38/7*m**3 = 0.
-2/5, 0, 2/11, 1/3
Let p(n) be the first derivative of -n**4/26 + 2*n**3/39 + 4*n**2/13 - 8*n/13 + 42. Suppose p(z) = 0. Calculate z.
-2, 1, 2
What is h in 40/7*h + 26/7*h**3 + 62/7*h**2 + 8/7 - 2*h**4 - 10/7*h**5 = 0?
-1, -2/5, 2
Let r(x) be the first derivative of 25*x**4/54 - 40*x**3/27 + 16*x**2/9 + 4*x - 44. Let i(t) be the first derivative of r(t). Factor i(o).
2*(5*o - 4)**2/9
Find m such that -5*m**2 - 2*m**3 + m**2 + 16*m**2 + 0*m**3 = 0.
0, 6
Let s(h) be the first derivative of h**6/240 + h**5/24 + h**4/6 + h**3/3 + 10*h**2 - 12. Let d(t) be the second derivative of s(t). Solve d(w) = 0 for w.
-2, -1
Let f(g) be the second derivative of -1/105*g**6 + 1/7*g**2 + 0 + 10*g + 0*g**4 + 2/21*g**3 - 1/35*g**5. Factor f(q).
-2*(q - 1)*(q + 1)**3/7
Let l(f) be the second derivative of 3*f**5/20 - 7*f**4/4 + 7*f**3 - 12*f**2 + 59*f. What is m in l(m) = 0?
1, 2, 4
Let r(d) be the third derivative of d**7/35 + 7*d**6/40 + d**5/20 - 7*d**4/8 - 3*d**3/2 - 682*d**2. Suppose r(u) = 0. What is u?
-3, -1, -1/2, 1
Let s(m) be the third derivative of m**7/105 + 23*m**6/10 + 216*m**5 + 18225*m**4/2 + 91125*m**3 + 99*m**2. Factor s(d).
2*(d + 3)*(d + 45)**3
Let x(p) = -15987*p**2 - 869*p - 19. Let y(a) = 10658*a**2 + 579*a + 13. Let b(j) = 5*x(j) + 7*y(j). Find g such that b(g) = 0.
-2/73
Let k(w) be the third derivative of -13*w**2 - 2/75*w**5 + 1/12*w**4 + 1/300*w**6 - 2/15*w**3 + 0*w + 0. Let k(r) = 0. Calculate r.
1, 2
Let k be (0 - (4 + 0)) + (-605)/(-110). Let u(p) be the first derivative of k*p + 3/16*p**4 + 1 - 3/8*p**2 - 1/2*p**3. Factor u(x).
3*(x - 2)*(x - 1)*(x + 1)/4
Let x = 177 + -191. Let r be (-44)/x - (-2)/((-2)/3). Suppose r*u**4 - 3/7*u**2 - 2/7*u**3 + 4/7 + 4/7*u = 0. What is u?
-1, 2
Suppose 0 = q + 2*o - 9, 3*q - 26 = 5*o + 12. Suppose q*b = 8*b + 6. What is w in -1/6*w**4 + 0 + 1/3*w**3 + 0*w + 1/2*w**b = 0?
-1, 0, 3
Let -60025*p + 245*p**2 - 1/3*p**3 + 14706125/3 = 0. Calculate p.
245
Let d(m) be the second derivative of -m**6/180 + m**5/60 + m**4/72 - m**3/18 + 7*m + 2. Determine o so that d(o) = 0.
-1, 0, 1, 2
Let i(q) be the third derivative of -q**5/30 + 3*q**4/4 - 8*q**3/3 + 4*q**2 - 9. Factor i(m).
-2*(m - 8)*(m - 1)
Factor 0*h + 0 - 3/2*h**2 - 3*h**4 - 15/4*h**3 - 3/4*h**5.
-3*h**2*(h + 1)**2*(h + 2)/4
Solve -7074*h - 274*h**2 - 10*h**3 - 262*h**2 + 1752 + 1164 = 0 for h.
-27, 2/5
Factor 0 + 0*h + 12/7*h**3 + 8/7*h**4 + 4/7*h**2.
4*h**2*(h + 1)*(2*h + 1)/7
Let b(m) be the first derivative of -5 + 125/4*m**4 + 175/3*m**3 - 70*m**2 + 20*m. Factor b(x).
5*(x + 2)*(5*x - 2)*(5*x - 1)
Let a(h) be the first derivative of 11/2*h**2 + 6 - 2*h - 5/3*h**3. Suppose a(w) = 0. What is w?
1/5, 2
Suppose 2*f + 14 = 2*k, -2*k - 3*f = -4*k + 19. Suppose -5*r**2 - 2 + 3*r**k + 5*r**2 - r**2 = 0. What is r?
-1, 1
Let x(y) = -y**4 - y**3 + y**2. Let t(a) = 8*a**4 + 11*a**3 - 2*a**2 + a. Let f(m) = -t(m) - 6*x(m). Find s such that f(s) = 0.
-1, -1/2, 0
Factor 16/21 - 6/7*a + 2/21*a**2.
2*(a - 8)*(a - 1)/21
Let s = -7103/6 - -1184. Let u(i) be the second derivative of i**5 + 10/3*i**3 - 6*i - 5/2*i**4 + 0 - s*i**6 - 5/2*i**2. Factor u(c).
-5*(c - 1)**4
Factor -475*n**5 - 2*n**3 + n**3 + 6*n**4 + 467*n**5 + 3*n**3.
-2*n**3*(n - 1)*(4*n + 1)
Let q(r) be the third derivative of r**6/720 + 7*r**5/60 + 9*r**4/16 + 10*r**3/9 - 108*r**2. Let q(i) = 0. Calculate i.
-40, -1
Let m(o) = -20*o**3 - 45*o**2 + 55*o + 5. Let k(y) = 31*y**3 + 68*y**2 - 83*y - 8. Let j(f) = -5*k(f) - 8*m(f). Factor j(r).
5*r*(r - 1)*(r + 5)
Factor -904 - 56*z - 4*z**2 - 972 - 5*z + 1812 - 7*z.
-4*(z + 1)*(z + 16)
Let y be 1/(1/(-4) + 0 - 0). Let a be 9/((-189)/12)*2/y. Determine i, given that -a*i**4 + 0 - 2/7*i**3 + 2/7*i + 2/7*i**2 = 0.
-1, 0, 1
Let a be ((-2)/(-4))/(2/8). Suppose v = a*l - 6, -5*l + 21 = -v + 6. Factor -5 + 6*z + 2 + l - 3*z**2.
-3*z*(z - 2)
Suppose -19*g + 4 = -15*g. Let a be 2 - (-1 + g - 0/4). Find l, given that 8/3*l + 2/3*l**4 + 4*l**a + 8/3*l**3 + 2/3 = 0.
-1
Let h be ((-48)/(-108))/((-40)/(-36)). Factor w - h + 1/5*w**4 - 3/5*w**2 - 1/5*w**3.
(w - 1)**3*(w + 2)/5
Let s be 6/24 + 21/12. Factor 3*b - 6*b + s*b**2 - 3*b.
2*b*(b - 3)
Suppose 0 = i + 5*d - 11, -5*d - 118 = -5*i - 33. Factor 10*t**4 + 22*t**3 - 4*t**4 + 601*t + i*t**2 - 609*t.
2*t*(t + 2)**2*(3*t - 1)
Factor -39 - 5*u**3 + 5*u - 233*u**2 + 97 + 42 + 133*u**2.
-5*(u - 1)*(u + 1)*(u + 20)
Let t(f) be the first derivative of f**4/4 + f**3 + f**2 - 4*f + 2. Let z(u) = u**3 + u. Let c(a) = -t(a) + 2*z(a). Determine k so that c(k) = 0.
-1, 2
Suppose 0 = n - 4*g + 11, -2*n - 4 = -4*g + 2. Let l be ((-20)/(-8))/(n/4). Determine d, given that d - 2 - 2*d + l*d + d**2 = 0.
-2, 1
Let n(t) be the first derivative of 1/8*t**4 + 2*t**2 - 2*t + 37 - 5/6*t**3. Factor n(m).
(m - 2)**2*(m - 1)/2
Let k(i) = -i**2 - 2. Let m(b) = b**2 + b + 1. Suppose 20 = -0*n - 2*n + 3*r, -4*r + 40 = -4*n. Let v(p) = n*m(p) - 5*k(p). What is s in v(s) = 0?
-2, 0
Let w be (-4)/(-22) + 560/1155. Let o(a) be the first derivative of 4 + w*a**2 + 2/3*a + 1/24*a**4 + 5/18*a**3. Suppose o(s) = 0. Calculate s.
-2, -1
Let p(w) be the third derivative of 0*w + 0*w**3 + 0*w**4 - 12*w**2 + 0 + 1/180*w**6 + 1/315*w**7 + 0*w**5. Factor p(c).
2*c**3*(c + 1)/3
Determine w, given that -624*w + 713 + 2962 - 7574 - 3*w**2 - 28549 = 0.
-104
Let u(r) be the second derivative of 0 - 1/24*r**4 - 28*r + 1/4*r**2 + 0*r**3. Factor u(g).
-(g - 1)*(g + 1)/2
Let x(n) be the third derivative of 0 - 1/270*n**5 + 3*n**2 + 1/108*n**4 + 0*n + 0*n**3 + 1/945*n**7 - 1/540*n**6. Solve x(a) = 0.
-1, 0, 1
Let g(x) be the second derivative of 1/24*x**4 - 9*x - 1/168*x**7 + 7/24*x**3 + 0 - 1/24*x**6 + 3/8*x**2 - 3/40*x**5. Solve g(l) = 0.
-3, -1, 1
Let y(k) be the third derivative of -k**8/840 + 2*k**7/175 + 44*k**2. Factor y(z).
-2*z**4*(z - 6)/5
Factor -17/4*v - 1/4*v**2 + 9/2.
-(v - 1)*(v + 18)/4
Find g such that -2*g - 13*g**2 + 27*g**3 + 2*g - 260*g**5 + 261*g**5 - 15*g**4 = 0.
0, 1, 13
Let j(b) be the second derivative of b**4/96 + 17*b**3/12 + 289*b**2/4 + 37*b - 2. Factor j(q).
(q + 34)**2/8
Let r = 1469 - 1465. What is j in -3/2*j + 0 + 0*j**3 + 3/2*j**5 + 3*j**r - 3*j**2 = 0?
-1, 0, 1
Suppose -5*k + 2*t + 3 = 0, 0 = -4*k - t + 6 - 1. Suppose h - k = 4. Factor 4*v**3 - 2*v**3 - 6*v**3 + 4*v**h.
4*v**3*(v - 1)*(v + 1)
Let a(p) be the first derivative of -2/11*p**4 + 0*p - 1/11*p**5 - 10 + 0*p**2 + 4/33*p**3. Determine m, given that a(m) = 0.
-2, 0, 2/5
Let g(h) = 5*h**5 - 7*h**4 - 9*h**3 + 16*h**2 - 5*h - 3. Let p(o) = -4*o**5 + 6*o**4 + 8*o**3 - 16*o**2 + 6*o + 2. Let r(s) = -2*g(s) - 3*p(s). Factor r(n).
2*n*(n - 2)*(n - 1)**2*(n + 2)
Let z(u) = u**4 - 11*u**3 - 32*u**2 - 30*u + 3. Let q(k) = 3*k**4 - 21*k**3 - 64*k**2 - 62*k + 7. Let m(p) = 6*q(p) - 14*z(p). Factor m(r).
4*r*(r + 2)**2*(r + 3)
Determine a, given that 32/5 + 36/5*a**2 - 56/5*a + 1/5*a**4 - 2*a**3 = 0.
2, 4
Find u, given that 1/3 + 0*u - 1/3*u**2 = 0.
-1, 1
Let n(u) be the second derivative of u**6/20 + 9*u**5/40 - 15*u**4/4 - 32*u**3 - 72*u**2 - 204*u. Factor n(a).
3*(a - 6)*(a + 1)*(a + 4)**2/2
Let z(j) be the first derivative of -2*j**5 - 175*j**4/16 - 65*j**3/3 - 155*j**2/8 - 15*j/2 - 89. Determine p, given that z(p) = 0.
-2, -1, -3/8
Let v(n) be the second derivative of -1/30*n**3 - 1/20*n**4 - 3/100*n**5 - 1/2*n**2 - 5*n + 0. Let h(b) be the first derivative of v(b). Solve h(k) = 0 for k.
-1/3
Suppose 43 + 88*l**2 + 170*l + 400*l**3 + 50 - 9 - 398*l**3 = 0. Calculate l.
-42, -1
Suppose -p = -0*p + 20. Let y be p/(-12)*12/10. Factor y*j**2 - 1/2*j + 0 + 2*j**4 - 3*j**3 - 1/2*j**5.
-j*(j - 1)**4/2
Let k be 8/18*(-6)/(-4). Let s = 215/663 + 2/221. Solve -2/3*c**3 + 1/3*c + 1/3*c**4 + s