 = 27*z - 44*z + 51. Suppose 0 = 3*t - 2*t + z*t. Determine l so that 4/3*l + t - 2*l**2 = 0.
0, 2/3
Let x(j) be the first derivative of -j**2 - 2/5*j**5 - 12 + 1/2*j**4 + 0*j + 2/3*j**3. Suppose x(g) = 0. What is g?
-1, 0, 1
Let q be 10*(-78)/(-45) - 48/4. Factor -2*s**2 + 2/3*s**4 - 8/3 + q*s - 4/3*s**3.
2*(s - 2)*(s - 1)**2*(s + 2)/3
Let s(u) be the second derivative of -u**8/16800 - u**7/700 - u**6/225 + 17*u**4/6 + 21*u. Let p(z) be the third derivative of s(z). Solve p(t) = 0.
-8, -1, 0
Suppose -96*j = -95*j - 2. Find w, given that 0*w + 13*w**2 - 6*w + 13*w**j - 29*w**2 = 0.
-2, 0
Suppose -5*f = 4*a - 24, 3*a + 9*f - 14*f = 18. Let n(s) be the third derivative of -1/4*s**4 - s**2 + 0 + 0*s + 3/20*s**5 - 1/40*s**a + 0*s**3. Factor n(x).
-3*x*(x - 2)*(x - 1)
Let o = 1569 + -1569. Let -2/5*z**2 - 2/5*z**5 - 6/5*z**4 - 6/5*z**3 + 0*z + o = 0. Calculate z.
-1, 0
Let r = -1140 + 3422/3. Let y(g) be the third derivative of -r*g**4 - 5*g**2 + 4/3*g**3 - 7/30*g**5 + 0 + 1/12*g**6 + 0*g. Let y(a) = 0. What is a?
-1, 2/5, 2
Factor 35*u**2 - 40*u + 0*u**3 + 3 - 83 - 5*u**3.
-5*(u - 4)**2*(u + 1)
Suppose 3*n = -4*g + 12, -4*g + 61*n = 63*n - 12. Factor 25*j**4 + j + 0 + 9*j**2 + 105/4*j**g.
j*(4*j + 1)*(5*j + 2)**2/4
Let y(l) = -6*l - 14. Let z be y(-3). Let -58*r**3 + 3*r**2 + 0*r**4 - z*r + 8*r + 3*r**2 + 54*r**5 - 6*r**4 = 0. Calculate r.
-1, -2/9, 0, 1/3, 1
Let n(a) be the third derivative of -a**5/210 - 2*a**4/21 - 16*a**3/21 + 48*a**2. Suppose n(l) = 0. Calculate l.
-4
Let w(o) be the third derivative of 1/105*o**7 - 1/30*o**5 + 1/4*o**4 - 1/20*o**6 + 0*o + 0 + 0*o**3 - 16*o**2. Suppose w(u) = 0. What is u?
-1, 0, 1, 3
Let k(c) be the second derivative of 0*c**4 + 29*c + 0*c**3 + 1/60*c**5 + 0*c**2 + 0 + 1/45*c**6 + 1/126*c**7. Find i, given that k(i) = 0.
-1, 0
Suppose 87*f - 2148 = -1800. Suppose -f*d**2 - 50/3 - 15*d - 1/3*d**3 = 0. What is d?
-5, -2
Let w = 7221/10543 + 6/811. Let u = w + -6/65. Determine f so that 18/5*f**3 + 0 - 12/5*f**2 - 12/5*f**4 + 3/5*f**5 + u*f = 0.
0, 1
Let p(b) = -b**2 - 14*b - 18. Let t be p(-12). Factor 3*m - t + 2*m - 9*m + 2*m**2.
2*(m - 3)*(m + 1)
Suppose -m = -41 - 1. Let y be (9/m)/((-27)/(-396)). Factor -2/7*c - 8/7*c**4 + 2/7 - y*c**3 - 18/7*c**2.
-2*(c + 1)**3*(4*c - 1)/7
Let g(v) be the first derivative of v**8/128 - 9*v**7/560 + v**6/160 + 5*v**2 - 24. Let c(l) be the second derivative of g(l). Let c(m) = 0. Calculate m.
0, 2/7, 1
Let n = -87/437 - -7/23. What is b in 2/19 + n*b**2 - 4/19*b = 0?
1
Let w = 772 + -769. Let v(o) be the first derivative of 5 + 2/21*o**w + 8/7*o - 5/7*o**2. What is t in v(t) = 0?
1, 4
Let s(d) be the third derivative of 1/10*d**6 + 4/3*d**3 + 7/6*d**4 + 8/15*d**5 + 0 + 0*d - 2*d**2. Factor s(g).
4*(g + 1)**2*(3*g + 2)
Let s(d) be the first derivative of 2/7*d**2 + 7 + 2/21*d**3 + 2/7*d. Factor s(z).
2*(z + 1)**2/7
Let r(i) = -7*i**2 - 55*i + 56. Let z(f) = 65*f**2 + 495*f - 505. Let s(d) = 55*r(d) + 6*z(d). Find w, given that s(w) = 0.
1, 10
Let k be ((-1)/2)/((-6)/(-72)) + 43/7. Factor k*n**5 + 0*n**3 - 3/7*n**4 + 0 + 0*n + 4/7*n**2.
n**2*(n - 2)**2*(n + 1)/7
Suppose 6*s - s + 11 = 2*o, -s = -2*o + 23. Let l(z) = z - 1. Let y be l(o). Factor -8 + 33*i**2 + 14*i**3 - 12*i - y*i - 15*i**2.
2*(i - 1)*(i + 2)*(7*i + 2)
Let f(g) = 675*g**4 - 763*g**3 + 95*g**2 - 5*g + 2. Let o(x) = -675*x**4 + 762*x**3 - 96*x**2 + 6*x - 3. Let a(v) = 3*f(v) + 2*o(v). Factor a(w).
3*w*(w - 1)*(15*w - 1)**2
Suppose 0 = 5*m + 75 - 225. Solve 13 + m*c**3 + 9*c + 51*c + 65*c**2 - 31*c**4 + 7 + 36*c**4 = 0 for c.
-2, -1
Let o = 5368 - 5368. Let b be 24/9 + -2 - 0. Suppose 0*j**2 - 2/3*j**3 + b*j + o = 0. What is j?
-1, 0, 1
Let r(m) be the second derivative of -7*m**6/15 - 48*m**5/5 - 203*m**4/6 + 22*m**3 - 136*m. What is p in r(p) = 0?
-11, -3, 0, 2/7
Let j(g) be the third derivative of -g**8/84 + 9*g**7/35 - 37*g**6/60 + 2*g**5/5 + 48*g**2. Determine h, given that j(h) = 0.
0, 1/2, 1, 12
Let u(j) be the first derivative of -2*j**5/15 + 7*j**4/6 - 10*j**3/3 + 3*j**2 + 84. Factor u(g).
-2*g*(g - 3)**2*(g - 1)/3
Factor 24/11*y - 2/11*y**2 + 90/11.
-2*(y - 15)*(y + 3)/11
Suppose 0 = 2*s + 3*j - 4, -j - 12 + 4 = -4*s. Let 3/5*c + 3/5*c**s + 0 = 0. What is c?
-1, 0
Let r(h) be the third derivative of -h**5/60 - h**4/3 + 10*h**3/3 + 2*h**2 - 19. Factor r(o).
-(o - 2)*(o + 10)
Let a(v) = v**2 + 7*v - 4. Let t be a(-8). Solve -q**3 - 2*q + 2*q + 2*q**2 - t*q + 3*q = 0 for q.
0, 1
Let c be 0*(-1)/(-1) + 0. Let a be c*(-1 + 4)/(-6). Suppose 0*g**5 - g**2 + 4*g - 4*g**5 + 8*g**4 - 7*g**2 + a*g**5 = 0. What is g?
-1, 0, 1
Let k be (-3)/(-6)*1*36. Factor -2 - k*u**2 + 12*u**2 - 18*u - 39*u**3 - 15*u**3 - 48*u**2.
-2*(3*u + 1)**3
Factor 328*c**3 - 2*c**5 - 5*c**4 - 312*c**3 + c**4.
-2*c**3*(c - 2)*(c + 4)
Solve -28*g + 138/5 + 2/5*g**2 = 0 for g.
1, 69
Let w = 3403 - 3401. Suppose 0 - 32/5*i**3 - w*i**5 + 0*i - 8/5*i**2 - 34/5*i**4 = 0. Calculate i.
-2, -1, -2/5, 0
Let j(i) be the first derivative of -4*i**2 + 0*i**4 - 4/5*i**5 + 4*i**3 - 10 + 0*i. What is h in j(h) = 0?
-2, 0, 1
Suppose -5*k - 2*a = -297, 3*k + 6*a = 2*a + 181. Let b = -115/2 + k. Factor -3/2*q + b*q**2 + 0.
3*q*(q - 1)/2
Let a(s) be the second derivative of 1/3*s**3 + 0*s**2 - 24*s + 0 + 1/24*s**4. Solve a(y) = 0.
-4, 0
Suppose -7*j = -45 + 17. Let f(l) be the second derivative of 0 - 4/5*l**2 + 4/15*l**3 - j*l - 1/30*l**4. Factor f(d).
-2*(d - 2)**2/5
Let n(u) = 13*u**4 - 18*u**3 + 7*u**2 - 12*u - 2. Let k(i) = -2*i**4 + 2*i**3 + i**2 + 1. Let j(a) = 6*k(a) + n(a). Factor j(f).
(f - 2)**2*(f - 1)**2
Factor -23*q**2 + 19/5*q**3 + 1/5*q**5 - 40*q + 100 + 11/5*q**4.
(q - 2)**2*(q + 5)**3/5
Let o(r) be the first derivative of 2*r**3/33 - 13*r**2/11 - 77. Solve o(p) = 0.
0, 13
Suppose 0*t - 12*t**2 + 27*t**4 - 15/2*t**5 + 0 - 18*t**3 = 0. What is t?
-2/5, 0, 2
Let u(f) = -27 + 2*f**3 - 8*f + 27 + 2*f**2. Let g(d) = d**3 + d**2 - 3*d. Let c(b) = 8*g(b) - 3*u(b). Find t such that c(t) = 0.
-1, 0
Let q(f) be the third derivative of -f**8/112 + f**7/14 - 9*f**6/40 + 7*f**5/20 - f**4/4 + f**2 - 4. Let q(a) = 0. Calculate a.
0, 1, 2
Suppose 3 - 3 = -n. Let -5*i**2 - 50*i + 2 - 159 + n*i**2 + 32 = 0. What is i?
-5
Suppose 139 = 14*h + 55. Let x(j) = j**3 - 7*j**2 + 6*j + 2. Let l be x(h). Factor -1/2*s**l + 0 - s.
-s*(s + 2)/2
Let d(n) = -n**2 + 7*n - 4. Let f be d(6). Suppose 0 = -f*j + j. Find k, given that -3*k**2 + j*k**2 + 5*k**3 - 2*k**3 + 0*k**3 = 0.
0, 1
Let j(o) be the second derivative of -3*o**5/140 - 19*o**4/28 - 5*o**3/2 - 51*o**2/14 + 140*o. Factor j(g).
-3*(g + 1)**2*(g + 17)/7
Factor -v**3 + 435*v**2 + 924*v + 127 + 77 + 12*v**3 + v**3.
3*(v + 2)*(v + 34)*(4*v + 1)
Let n(h) be the first derivative of h**6/15 + 4*h**5/5 + 17*h**4/5 + 104*h**3/15 + 37*h**2/5 + 4*h + 17. Determine z so that n(z) = 0.
-5, -2, -1
Let f be ((-2)/(-40))/(4/(24/126)). Let i(d) be the third derivative of 0*d**3 + 0 + f*d**5 + 0*d + 1/56*d**4 - 13*d**2. Factor i(c).
c*(c + 3)/7
Let q(v) be the first derivative of -5/2*v**2 + 5/4*v**4 + 48 - 25/3*v**3 + 25*v. Factor q(s).
5*(s - 5)*(s - 1)*(s + 1)
Solve r - 4*r - 20*r - 3*r**2 + 50*r = 0 for r.
0, 9
Let k(s) = -36*s**5 + 10*s**4 - 2*s**3 + 4*s. Let w(u) = 36*u**5 - 9*u**4 + u**3 - 3*u. Let q(a) = -3*k(a) - 4*w(a). Suppose q(i) = 0. What is i?
-1/6, 0, 1/3
Let c be (80/(-30))/((-12)/18). Let j(g) be the first derivative of g**3 + 0*g + 0*g**2 - 1 + 3/4*g**c. Determine o so that j(o) = 0.
-1, 0
Let f(m) be the third derivative of 0 + 3/20*m**5 - m**3 + 0*m + 1/8*m**4 + 13*m**2 - 1/70*m**7 - 1/40*m**6. Suppose f(h) = 0. Calculate h.
-2, -1, 1
Let w(m) be the third derivative of -m**5/210 - 3*m**4/14 - 3*m**2 - 4. Determine f so that w(f) = 0.
-18, 0
Let d(m) be the first derivative of -25/4*m**3 - 11 - 3/4*m - 15/4*m**2. Let d(p) = 0. Calculate p.
-1/5
Let q(b) = -b**2 + 6. Let w be q(3). Let g be (0/(-1 - -2 - 0))/w. Find h, given that -2/9*h**3 + g*h**2 + 0 + 2/9*h**4 + 0*h = 0.
0, 1
Solve 0*u - 3/4*u**5 - 15/4*u**4 + 0 + 6*u**2 - 3/2*u**3 = 0.
-4, -2, 0, 1
Suppose -72 = -3*y - 0*y. Factor -20*c - 4 - 2*c**4 - y*c**2 - 4 + 2 + 0*c**4 - 12*c**3.
-2*(c + 1)**3*(c + 3)
Let 7/5*x**3 - 4/5 - x**2 - 16/5*x = 0. What is x?
-1, -2/7, 2
Let b be (-8)/(220/(-5) + 20). Factor 0*k**2 - b*k**3 + 1/3*k - 1/6*k**4 + 1/6.
-(k -